{"id":"ea8a9bbe-b087-4ea2-8806-8489f1df3852","arxiv_id":"2506.11211","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"For a specifically chosen non-uniform magnetic field on the sphere, Laughlin quasiholes acquire an analytically computed, interaction-generated energy dispersion whose functional form is exact up to a fitted overall scale.","lead":"A specially shaped non-uniform magnetic field on a sphere lets Laughlin quasiholes acquire an interaction-generated energy dispersion, even though the electron bands remain perfectly flat. The authors derive an exact mapping to the uniform-field problem and an analytic formula for the dispersion, whose functional form is fixed up to one fitted scale.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The analytic 8th-power dispersion form in Eq. (19) rests on the plasma-screening assumption of App. E; the exact mapping is solid, but the factorization into a single R-independent amplitude a_3 is unproven.","rationale":"Read in good faith: the paper's exact mapping from the non-uniform field to a dilated interaction in a uniform field (Eq. 10) is a rigorous operator identity, and the ED spectra support the qualitative claim that interaction alone generates nonzero anyon dispersion. The quantitative claim—the specific 8th-power form and the factored xi-dependence—is derived in App. E under the plasma-screening assumption. That assumption is standard for Laughlin states but is not proven here; it is the single place where the analytic formula could fail without undermining the exact mapping or the qualitative physics. The fitted amplitude a_3 is an acknowledged limitation but does not by itself threaten the central claim. A direct Monte Carlo test of the integral in (D47) would settle whether the screening replacement holds and would distinguish the predicted functional form from a low-order polynomial fit to N=8 data. I agree with the reader's weakest_assumption and recommend keeping the CONDITIONAL verdict.","tokens_in":22411,"tokens_out":19647,"duration_ms":221631,"concrete_test":"Perform Monte Carlo evaluation of the Laughlin quasihole pair correlation function at nu=1/3 (e.g., using the method of Fulsebakke et al., SciPost 14, 149 (2023)) for N=20, 50, and 100 particles on the sphere. Compute the exact integral in Eq. (D47) for the V3 pseudopotential: v^R_xi = (1/R^8) ∫ dµ(w) [1 + (R^2−1)/4 d^2(w,−xi)]^8 f_SP(w,w), for several R and xi. Test whether (v^R_xi − a_0(R)) / [(1+R^2|xi|^2)/(R(1+|xi|^2))]^8 is independent of xi and R for each N and converges to a constant as N→∞. If it does, the screening replacement is validated; if the residual N- or xi-dependence is significant, Eq. (19) fails and the analytic dispersion form is not exact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central quantitative claim—Eq. (19), epsilon^R_kappa = a_0(R) − a_3 [(1+kappa+R^2(1−kappa))/(2R)]^8—rests on the plasma-screening assumption in Appendix E. There, g_xi(z1,z2) is assumed to depend only on d(z1,xi)/l_B, d(z2,xi)/l_B, and d(z1,z2)/l_B, and to saturate beyond a few magnetic lengths, so that the slowly varying factor h_R(z) can be replaced by h_R(xi) for particles contributing to the dispersion. This replacement converts the exact two-body expression into the factored power-law form with a single R- and xi-independent amplitude a_3. If the quasihole pair correlation function is not screened on the magnetic-length scale, the xi-dependence of v^R_xi acquires uncontrolled contributions from regions far from the quasihole, where h_R(z) differs from h_R(xi); the exponent 8 and the factorization would then not follow. The N=8 ED comparison (Fig. 3) is a consistency check, not a first-principles verification: with a_0(R) and a_3 fitted at each R, a smooth 8th-power curve can represent 9 points even if the true thermodynamic form is different. Thus the load-bearing step for the analytic formula is the screening assumption, not the exact mapping (Eq. 10), which appears rigorous.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the lowest Landau level (LLL) on the sphere in the presence of a rotationally symmetric, non-uniform magnetic field parameterized by R, which breaks the SU(2) rotation symmetry down to U(1) but keeps the single-particle dispersion exactly flat. The authors show that for their chosen magnetic potential Q_R, any p-body correlation function in the Laughlin quasihole space maps exactly to a corresponding correlation function in a uniform field with a rescaled interaction (Eq. 10). Using this mapping and a plasma-screening argument for the quasihole pair correlation function, they derive the thermodynamic-limit anyon dispersion ε^R_κ = a0(R) − a3 [(1+κ+R^2(1−κ))/(2R)]^8 for short-range V3 interactions (Eq. 19), up to an overall amplitude a3 and offsets a0(R), which are fitted to N=8 exact diagonalization data. They also give a more involved expression for Coulomb interactions (Eq. E10). The central conceptual message is that interaction alone, in the absence of continuous magnetic translation symmetry, can generate a nonzero dispersion for anyons.","tokens_in":22689,"tokens_out":24827,"duration_ms":273083,"significance":"If the result holds, the paper provides a concrete and analytically tractable demonstration that inhomogeneous magnetic field (i.e., inhomogeneous quantum geometry) can generate anyon dispersion without introducing single-particle dispersion — a mechanism of direct relevance to fractional quantum anomalous Hall systems and ideal flat bands. The main strengths are: (i) the exact mapping in Eq. (10) and App. B/C is derived rigorously for the two-body interaction and does not rely on the uncontrolled approximations used in earlier work; (ii) the model preserves exact flatness of the single-particle dispersion by construction; (iii) the paper is honest about the role of the fitted amplitude a3 and offsets a0(R); (iv) the predicted functional form in Eq. (19) is a concrete, falsifiable statement that can be tested at larger system sizes or with Monte Carlo. The thermodynamic-limit formula is the least certain part, since it rests on a plasma-screening assumption that is stated but not fully derived; nevertheless, the paper sets a clear quantitative target for future checks.","major_comments":[{"comment":"The load-bearing step for the analytic dispersion formula is the plasma-screening assumption that g_ξ(z1,z2) depends on distances only through d(z1,ξ)/l_B, d(z2,ξ)/l_B, and d(z1,z2)/l_B, and saturates beyond a few magnetic lengths, so that h_R(z) can be replaced by h_R(ξ) for all contributing configurations. This is stated as an expectation, not derived, and no bound on the corrections is given. Because Eq. (19) is the central quantitative claim, I ask the authors to substantiate this factorization in one of two concrete ways: (a) perform a Monte Carlo evaluation of the exact expression (D36) using the uniform-field pair correlation g_SP, which would determine a3 independently of the ED fit and directly test whether the R and ξ dependence factorizes as (η^R_ξ)^8; or (b) provide finite-size scaling of the ED-extracted a3 (e.g., for N=6,8,10) establishing its independence of N and R. Without such a check, the excellent agreement in Fig. 3 cannot be taken as a first-principles verification, since a0(R) and a3 are fitted to the same 9-point spectra.","section":"Appendix E, Eqs. (18)–(19)"},{"comment":"The fitting procedure is underspecified. The text states that a3 is determined by fitting the bandwidth, but it does not say whether a3 is a single global parameter across all R and across both ε^R_M and v^R_ξ, or whether it is fitted separately for each R. If a3 is fit separately at each R, then the claimed R-independence of a3 is assumed rather than demonstrated. Please report the fitted values of a0(R) and a3, and show either a comparison with a single fixed a3 or the extracted a3(R) values to demonstrate R-independence.","section":"Fig. 3 and text after Eq. (18)"},{"comment":"The exact mapping is proven in App. B for two-particle density-density interactions, and the paper states in the main text that it generalizes to any p-body correlation function, with the justification relegated to a remark attached to the statement. Since the generalization to p-body operators is advertised in the abstract and used to motivate future applications (e.g., multi-anyon bound states), the authors should either provide the explicit p-body generalization in an appendix or soften the claim. This does not affect the two-body dispersion result, but it is part of the paper's advertised scope.","section":"Main text, Eq. (10) and generalization to p-body operators"}],"minor_comments":[{"comment":"The sentence attributing higher energy to quasiholes with large angular momentum whose wavefunctions have more weight on the north pole is potentially confusing, because the coherent-state convention in Eqs. (15)–(16) and App. D relates ξ=∞ to the lowest angular momentum state m=−l. Please clarify the correspondence between ξ, m, and the pole positions, and reconcile it with the energy ordering from Eq. (19).","section":"After Eq. (12)"},{"comment":"The inversion formula ε^R_κ = v^R_ξ with ξ = sqrt((1−κ)/(1+κ)) assumes that ξ is real and non-negative; this should be stated explicitly, together with the azimuthal symmetry that determines the phase.","section":"Eq. (16)"},{"comment":"The caption contains a duplicated reference to Eq. (18) ('Eq. (18), Eq. (18)'), which should be corrected.","section":"Fig. 3 caption"},{"comment":"The plasma-screening argument cites an empty reference ('[]') after 'screened over a distance ∼l_B'; a proper citation to the plasma analogy for the Laughlin wavefunction should be added.","section":"Appendix E, Eq. (E1)"},{"comment":"The abstract says the dispersion is 'computed exactly, up to an overall scaling constant', but the offsets a0(R) are also fitted to the numerics; the wording should acknowledge that both a3 and a0(R) are determined by fitting, so the exact part is the functional dependence on κ and R, not the overall scale or offset.","section":"Abstract and conclusion"}],"recommendation":"major_revision","confidential_remarks":"The exact mapping in Eq. (10) is a solid and valuable contribution, and the paper is well within the scope of the journal. My main concern is that the central thermodynamic-limit formula, Eq. (19), rests on a screening/factorization assumption that is not proven and is validated only by fits to a single small system size. This seems fixable with additional Monte Carlo or finite-size scaling analysis, so I recommend major revision rather than rejection. I would also encourage the authors to make the fitting procedure completely transparent, as the R-independence of a3 is one of the key predictions of the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The exact mapping in Eq. (10) is the real contribution, and I see no problem with it. For the specially chosen field Q_R, the transformation T_R is diagonal, so every p-body correlation function in the quasihole subspace maps exactly onto the uniform-field problem with a dilated interaction. That is rigorous and new, and it fixes the uncontrolled approximation in ref. [24] rather than just patching it. The dispersion formula in Eq. (19) sits on top of that mapping, and the paper is honest that it is exact only up to a fitted overall scale a3 and an offset a0(R).\n\nThe soft spot is the screening assumption in App. E. The 8th-power exponent itself comes from the exact transformation of the V3 pseudopotential, not from the fit. But to get a single R-independent a3, the pair correlation function g_xi has to be supported within a few magnetic lengths of the quasihole, so that the slowly varying factor h_R(z) can be evaluated at xi and pulled out of the integral. If that screening fails, the xi-dependence picks up uncontrolled contributions from far away and the factorization in Eq. (19) does not follow. The N=8 ED comparison is a consistency check, not a first-principles verification; with a3 and a0(R) fitted, a smooth curve can represent nine points. I still think the screening assumption is physically reasonable for Laughlin states, but it is not proved here.\n\nThe Coulomb case has the same structure, with more fitted parameters, but the ED agreement is good. The coherent-state path integral gives a clean picture of why a purely potential term produces azimuthal motion. The citation pattern is fine; the contrast with ref. [24] is explicit rather than ex silentio. Minor issues: an empty citation bracket in App. E for the plasma analogy, and no code or data shipped. I'd ask for both in revision.\n\nThere is nothing here that makes me doubt the qualitative result: interaction alone can generate anyon dispersion in an inhomogeneous field. The exact mapping is a solid contribution, and the quantitative formula is a plausible derived result whose main caveat is clearly labeled. This deserves a serious referee. Send it to review.","headline":"Exact mapping in Eq. (10) is rigorous and new; the 8th-power dispersion is a plausible derived result with a screening assumption and a fitted amplitude.","tokens_in":23238,"tokens_out":3993,"would_cite":true,"duration_ms":45271,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Interactions alone can give Laughlin anyons a nonzero dispersion on a sphere with a non-uniform magnetic field; the exact thermodynamic-limit dispersion is an eighth-power law.","keywords":["anyon dispersion","Laughlin quasiholes","non-uniform magnetic field","spherical geometry","lowest Landau level","exact mapping","fractional quantum anomalous Hall effect","thermodynamic limit"],"falsifier":"Run exact diagonalization for $N=10$ electrons at flux $2s=28$ with interaction $V_1+\\epsilon V_3$ at $R=1.2$ and $R=1.4$, extract the quasihole band energies $\\varepsilon^R_M$, and form the ratio $(\\varepsilon^R_\\kappa-a_0(R))/[(1+\\kappa+R^2(1-\\kappa))/(2R)]^8$; if the ratio is not the same constant $a_3$ for both $R$ values across the whole band, then the magnetic-length screening replacement used to derive Eq. (18) is quantitatively wrong and the claimed exact thermodynamic-limit formula fails.","tokens_in":22190,"feed_emoji":"🧲","tokens_out":26712,"duration_ms":247803,"temperature":0.7,"pith_summary":"The paper asks whether interactions alone can make the anyonic quasiparticles of a fractional quantum Hall state disperse, in a situation where continuous magnetic translation symmetry is broken but the single-particle spectrum is still perfectly flat. It answers yes, on the sphere: a specially chosen non-uniform magnetic field, concentrated at one pole, breaks the SU(2) rotation symmetry down to U(1) while leaving the lowest Landau level dispersionless. For this field profile, every $p$-body correlation function in the Laughlin quasihole space maps exactly onto the uniform-field one, so the interaction-generated potential felt by a quasihole can be computed analytically. In the thermodynamic limit this yields an explicit eighth-power dispersion $\\varepsilon^R_\\kappa=a_0(R)-a_3[(1+\\kappa+R^2(1-\\kappa))/(2R)]^8$ in the rescaled angular momentum $\\kappa$, showing that an inhomogeneous magnetic field alone can generate anyon dispersion. If the result holds up, it demonstrates a concrete mechanism -- non-uniform quantum geometry acting as a spatially varying potential -- that is expected to transfer to periodic settings relevant to fractional Chern insulators.","feed_headline":"Lopsided magnetic field gives anyons an exact eighth-power dispersion","feed_subtitle":"With a special lopsided field, quasihole energies follow an exact eighth-power law: interactions alone create dispersion","key_machinery":"The load-bearing construction is the special non-uniform magnetic potential $Q_R(|z|)=2\\ln(1+|z|^2)-2(s+1)\\ln(1+|z|^2/R^2)$ on the stereographically projected sphere. Its defining property is that the similarity transformation between non-uniform and uniform LLL operators, $\\hat T_R=\\exp(\\tfrac12\\sum_m \\beta^R_m \\hat c^\\dagger_m \\hat c_m)$, collapses to $\\hat T_R=R^{(s+1)N+L_z}$, a function of total particle number and angular momentum only; this makes the action of $\\hat T_R$ on any $p$-body correlation function evaluable from conserved quantum numbers. A second identity, $V(d(z_1,z_2))\\to V(Rz_1,Rz_2)$ with $d(Rz_1,Rz_2)=R\\sqrt{h_R(z_1)h_R(z_2)}\\,d(z_1,z_2)$ and $h_R(z)=(1+|z|^2)/(1+R^2|z|^2)$, absorbs the non-uniform field exactly into a dilation of the interaction. To turn the resulting effective potential into a dispersion, the quasihole states are represented as SU(2) spin coherent states $|\\Psi_\\xi\\rangle$, the potential $v^R_\\xi$ is computed from the uniform-field pair correlation function, and the $L_z$-resolved energies are recovered by the Bernstein-polynomial inversion formula (the exact linear relation between a polynomial's Bernstein coefficients and its sampled values), which in the thermodynamic limit simplifies to $\\xi=\\sqrt{(1-\\kappa)/(1+\\kappa)}$. The final analytic evaluation of $v^R_\\xi$ in the thermodynamic limit assumes that the quasihole pair correlation function is screened over the magnetic length, so that slowly varying weight factors can be pinned to the quasihole position $\\xi$.","core_discovery":"The paper studies the $\\nu=1/3$ Laughlin state on the sphere with one quasihole, in the presence of a one-parameter family of non-uniform radial magnetic fields $B_R$ generated by the potential $Q_R(|z|)=2\\ln(1+|z|^2)-2(s+1)\\ln(1+|z|^2/R^2)$. For this field the single-particle lowest Landau level remains perfectly flat, while the SU(2) rotation symmetry of the sphere is broken down to the U(1) of rotations about the $z$-axis, so the quasihole energies can be labelled by $L_z$. The central result is an exact mapping: in the quasihole space, the non-uniform-field Hamiltonian with interaction $V(z_1,z_2)$ equals the uniform-field Hamiltonian with the dilated interaction $V(Rz_1,Rz_2)$, and the chord distance rescales as $d(Rz_1,Rz_2)=R\\sqrt{h_R(z_1)h_R(z_2)}\\,d(z_1,z_2)$. The invertible but non-unitary transformation that implements this map, $\\hat T_R=R^{(s+1)N+L_z}$, is a function of conserved quantum numbers alone, so any $p$-body correlation function of the quasiholes is obtained exactly from uniform-field data. In the thermodynamic limit, using the plasma screening of the quasihole pair correlation function over a magnetic length, the effective potential felt by a quasihole at position $\\xi$ becomes $v^R_\\xi=a_0(R)-a_3[(1+R^2|\\xi|^2)/(R(1+|\\xi|^2))]^8$, and inverting the coherent-state relation yields the anyon dispersion $\\varepsilon^R_\\kappa=a_0(R)-a_3[(1+\\kappa+R^2(1-\\kappa))/(2R)]^8$ with $\\kappa=2M/N\\in[-1,1]$. This establishes, within the model, that interaction alone converts a spatially varying magnetic field into a dispersive energy for anyons while the single-particle spectrum stays flat.","pith_inferences":["The exact mapping should hold for any quasihole sector built from $V_1$ zero modes, not just a single quasihole, so multi-anyon observables -- including interactions between two quasiholes and any tendency toward bound states -- in a non-uniform field could be computed from uniform-field data by the same argument.","The eighth-power law implies a sharp numerical test beyond the paper's $N=8$ diagonalizations: for fixed $R>1$, the rescaled quantity $(\\varepsilon^R_\\kappa-a_0(R))(2R)^8/(1+\\kappa+R^2(1-\\kappa))^8$ should approach a single constant $a_3$ as $N$ grows, so finite-size exact diagonalization on larger systems could locate the breakdown of the magnetic-length screening assumption.","The spin-coherent-state picture suggests a dynamical probe: a quasihole initially localized at latitude $\\theta$ should precess around the azimuth with a frequency set by the derivative $\\partial\\varepsilon^R_\\kappa/\\partial\\kappa$ at $\\kappa=\\cos\\theta$; time-resolved imaging of the quasihole position would then measure the dispersion directly even where individual $L_z$ levels are not resolved."],"forward_implications":["Any $p$-body correlation function in the Laughlin quasihole space at non-uniform field $R$ can be evaluated exactly from the uniform-field correlation function, so effective few-anyon physics in an inhomogeneous background becomes analytically accessible.","Within this model, the quasihole moves azimuthally at constant latitude -- the coherent-state Lagrangian is that of a spin $N/2$ in a potential depending only on $S_z$ -- so the dispersion is a precession spectrum rather than a two-dimensional band, and itinerant-anyon phases such as anyon superconductivity are not expected in this geometry.","The mechanism -- non-uniform quantum geometry generating a spatially varying interaction potential -- is expected to transfer to periodic non-uniform fields on the torus, the setting relevant to fractional Chern insulators and FQAHE materials, where real dispersion could drive itinerant-anyon phases such as anyon superconductors.","For a residual $V_3$ pseudopotential, the thermodynamic-limit potential is exactly $a_0(R)-a_3(\\eta^R_\\xi)^8$ with $\\eta^R_\\xi=(1+R^2|\\xi|^2)/(R(1+|\\xi|^2))$, and higher pseudopotentials contribute the higher even powers $(\\eta^R_\\xi)^{2(2n+2)}$; for Coulomb interaction the same screening argument yields an elliptic-integral formula instead of the power law."],"supporting_citations":[{"why":"Supplies the spherical geometry with a magnetic monopole and the lowest-Landau-level basis on which the whole construction is built.","marker":"[55]"},{"why":"Provides the magnetic-potential formalism and the LLL wavefunctions on the sphere that the chosen field profile QR generalizes.","marker":"[68]"},{"why":"Defines the pseudopotential interactions whose V1 zero modes are exactly the quasihole states whose dispersion is studied.","marker":"[57]"},{"why":"Gives the root-configuration description used to label the N+1 quasihole zero modes by angular momentum Lz.","marker":"[58]"},{"why":"Introduced the mapping of ideal flat bands to a non-uniform-field LLL and used an uncontrolled approximation that the present exact mapping replaces.","marker":"[24]"},{"why":"Provides the Monte Carlo method used to compute the quasihole pair correlation function in the uniform field for the thermodynamic-limit results.","marker":"[62]"},{"why":"Supplies large-system Monte Carlo data for the same pair correlation function used to compare with the analytic thermodynamic-limit formula.","marker":"[63]"}],"fun_headline_variants":["Exact eighth-power anyon dispersion from a lopsided field","Lopsided field on sphere yields exact anyon energy law","Interaction alone gives anyons a precise eighth-power dispersion","Non-uniform field breaks symmetry to give anyons exact dispersion","Quasihole energies follow an exact eighth-power law on sphere"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation of the eighth-power dispersion assumes that the quasihole pair correlation function $g_\\xi(z_1,z_2)$ is screened over a magnetic length, meaning that correlations decay to their background value within a few magnetic lengths, so the slowly varying factor $h_R(z)$ inside the interaction integral can be replaced by its value $h_R(\\xi)$ at the quasihole position; if this plasma-screening assumption fails at the system sizes or field non-uniformities considered, the specific power-law form in Eq. (18) would not hold.","fun_headline_variants_meta":{"raw":{"variants":["Exact eighth-power anyon dispersion from a lopsided field","Lopsided field on sphere yields exact anyon energy law","Interaction alone gives anyons a precise eighth-power dispersion","Non-uniform field breaks symmetry to give anyons exact dispersion","Quasihole energies follow an exact eighth-power law on sphere"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000323,"raw_usage":{"total_tokens":1990,"prompt_tokens":1293,"completion_tokens":697,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":909,"completion_tokens_details":{"reasoning_tokens":612}},"tokens_in":909,"tokens_out":697,"duration_ms":7172,"temperature":1.0,"reasoning_tokens":612,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T04:14:27.327850+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run exact diagonalization for $N=10$ electrons at flux $2s=28$ with interaction $V_1+\\epsilon V_3$ at $R=1.2$ and $R=1.4$, extract the quasihole band energies $\\varepsilon^R_M$, and form the ratio $(\\varepsilon^R_\\kappa-a_0(R))/[(1+\\kappa+R^2(1-\\kappa))/(2R)]^8$; if the ratio is not the same constant $a_3$ for both $R$ values across the whole band, then the magnetic-length screening replacement used to derive Eq. (18) is quantitatively wrong and the claimed exact thermodynamic-limit formula fails.","supporting_citations":[{"cited_title":"Notes on the Squashed Sphere Lowest Landau Level","cited_arxiv_id":"1909.08042","evidence_quote":"Provides the magnetic-potential formalism and the LLL wavefunctions on the sphere that the chosen field profile QR generalizes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduced the mapping of ideal flat bands to a non-uniform-field LLL and used an uncontrolled approximation that the present exact mapping replaces."},{"cited_title":"Girvin, Physical Review B30, 558 (1984)","cited_arxiv_id":null,"evidence_quote":"Provides the Monte Carlo method used to compute the quasihole pair correlation function in the uniform field for the thermodynamic-limit results."},{"cited_title":"Fulsebakke, M","cited_arxiv_id":null,"evidence_quote":"Supplies large-system Monte Carlo data for the same pair correlation function used to compare with the analytic thermodynamic-limit formula."}],"review_version":1}