{"id":"c00aafb5-af2b-4d3a-83c4-d87604b1bf91","arxiv_id":"2507.03154","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Domain growth in the disordered long-range Ising model is logarithmic in 1D for all interaction ranges, while in 2D the growth law depends on interaction range and disorder strength, ranging from disorder-suppressed power laws to logarithmic growth and dynamical freezing.","lead":"This paper uses computer simulations to show how order grows in magnetic materials where long-range spin interactions compete with random pinning fields. The results reveal that one-dimensional systems always slow to logarithmic growth, while two-dimensional systems can either resist disorder, freeze, or fall into the same logarithmic slowdown depending on the interaction range and disorder strength.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Logarithmic-growth conclusion rests on a scaling collapse with a free per-disorder length ℓ(Δ); the same procedure can accommodate non-logarithmic growth over the observed R-range, so an independent direct fit is required.","rationale":"The paper is honest about its own limits: it explicitly leaves the asymptotic regime open for σ < 1 at R ≤ 100, and it correctly disclaims dynamical freezing as only 'suggestive.' The remaining positive claims — the 1D α(σ) values and the 2D σ = 3 logarithmic behavior with ψ ≈ 1.23 — all pass through the same scaling-collapse machinery. That machinery is the least secure link because ℓ(Δ) is chosen per data set to force overlap, and ψ = 1/α is only exact in the asymptotic regime where the subtracted zbar is negligible. In the key 2D plot, the data barely leave the crossover region, so the power-law fit is not a sharp test of logarithmic growth. The direct fit of R(t) to the logarithmic form, without per-Δ ℓ shifts, is the natural check: if it produces a common α consistent with 1/ψ, the conditional verdict could be upgraded; if not, the CONDITIONAL verdict should stand or be tightened. This assessment aligns with the reader's identified weakest assumption, so the reader's CONDITIONAL verdict remains unchanged.","tokens_in":18432,"tokens_out":15239,"duration_ms":191471,"concrete_test":"Take the 2D σ = 3, Δ ≤ T data used in Fig. 10(f)/Fig. 11 and fit, for each disorder Δ separately, the raw R(t) to R(t) = A_Δ [ln(t/τ_Δ)]^α, first with α shared across all Δ and then with α free per Δ, using a bootstrap over the 25 disorder realizations. Accept the logarithmic claim only if the shared-α fit is consistent with the per-Δ fits within bootstrap uncertainty and the resulting α agrees with 1/ψ from the collapse. If allowing α to vary per Δ significantly improves the fit, or if the direct fit rejects R ∼ (ln t)^α, then the collapse-based α is an artifact of the free ℓ(Δ) shifts rather than a confirmed growth law.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim — logarithmic growth with α = 1/ψ — is established through the Lippiello et al. collapse: plot zeff − zbar versus R/ℓ(Δ), with ℓ(Δ) chosen separately for each disorder strength to force overlap, and fit zeff − zbar = a(R/ℓ)^ψ (Eq. 13; Figs. 5 and 11). This is the only quantitative evidence for the headline conclusion. The assumption is load-bearing because: (i) ℓ(Δ) is a free parameter for every curve, so the collapse has limited discriminative power; (ii) the relation α = 1/ψ is an asymptotic one, following from R ∼ (ln t)^α only when zeff − zbar ≫ zbar, but in the 2D σ = 3 case the collapsed data in Fig. 11 reach only zeff − zbar ≈ 2 with zbar = 2, placing essentially the whole fit in the crossover region rather than in the asymptotic activated regime; and (iii) no error bars or bootstrap estimates are reported for ψ, so the quoted ψ ≈ 1.23 versus the NN value ≈ 1.5 is not statistically secured. The same caveat applies to the 1D α values, although there zeff − zbar reaches about 8, making the asymptotic limit more plausible. If the assumed scaling form is not uniquely forced by the data, then the extracted α(σ) values and the claim that long-range interactions reduce the growth exponent are not established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports Monte Carlo simulations of domain growth in the random-field long-range Ising model in one and two dimensions after a deep quench. It recapitulates the authors' earlier 1D result that growth is asymptotically logarithmic for all sigma > 0 with alpha(sigma) below the nearest-neighbor value alpha = 2, and presents new 2D simulations. For Delta <= T and sigma = 0.6, 0.9 the data show disorder-independent growth up to R <= 100, while for sigma = 3 a Lippiello-type collapse of the effective exponent is used to infer logarithmic growth with barrier exponent psi ~ 1.23. For Delta > T the dynamics is extremely slow and is interpreted as possible dynamical freezing. Dynamical scaling and superuniversality of C(r,t) are also checked.","tokens_in":18768,"tokens_out":11197,"duration_ms":121130,"significance":"If established, these results would extend the Huse-Henley activated-dynamics scenario to long-range disordered ferromagnets and would give quantitative guidance on when long-range interactions dominate disorder during coarsening. The paper is transparent about its main limitation for sigma < 1 in 2D, where only scales up to R ~ 100 are accessible, and it uses an Ewald-type summation for the long-range interactions. However, the central quantitative claims---alpha < 2 in 1D and psi ~ 1.23 for sigma = 3 in 2D---rest on a scaling collapse with a free per-disorder crossover length and are not supported by error bars or direct fits. The 2D sigma = 3 fit is especially fragile because it lies mostly in the crossover region rather than in the asymptotic activated regime.","major_comments":[{"comment":"The exponents alpha(sigma) and psi are extracted by plotting zeff - zbar against R/ell(Delta), where ell(Delta) is chosen separately for each disorder strength to force data collapse, and then fitting zeff - zbar = a(R/ell)^psi. Because ell is a free parameter per curve and no quantitative collapse metric or uncertainty is reported, this test has limited ability to distinguish logarithmic growth from other slowly varying growth laws over the simulated window. In addition, in the asymptotic activated regime Eq. (13) is precisely the form implied by R ~ (ln t)^alpha with alpha = 1/psi, so the fit is not an independent confirmation of logarithmic growth. I ask the authors to report direct fits of R(t) to a logarithmic law for each Delta, to give bootstrap estimates of the exponents, and to show the fitted range explicitly.","section":"Sections 4-5, Eq. (13), Figs. 5 and 11"},{"comment":"The evidence for logarithmic growth at sigma = 3 in 2D is not yet asymptotic. With zbar = 2, the collapsed data extend only to zeff - zbar ~ 2, so the entire fitted region has zeff - zbar comparable to zbar rather than much larger than it; the asymptotic activated regime is not reached. Since the 2D results are averaged over only 25 runs and no error bars or confidence intervals are displayed, the quoted psi ~ 1.23 (versus the nearest-neighbor value ~ 1.5) is not statistically secured. Please either provide additional simulation data at larger L and longer times, or present a careful bootstrap or chi-square analysis of the collapse and fit range before claiming logarithmic growth.","section":"Section 5, Fig. 11"}],"minor_comments":[{"comment":"The Metropolis transition rate contains an explicit factor N^{-1} in addition to min(1, exp(-Delta E/T)); since time is measured in Monte Carlo steps, please clarify whether this factor is intentional or a typographical error.","section":"Eq. (4)"},{"comment":"The phrase 'Except in D = 1' before Eq. (6) appears to be a slip; Eq. (6) is the exact 1D Hurwitz-zeta expression, while Ewald summation is used in D > 1.","section":"Section 3, Eq. (6)"},{"comment":"For sigma = 0.6 the text says growth 'initially follows the BR regime, characterized by zeff ~ 1 + sigma, and gradually approaches the asymptotic value z = 4/3,' but the caption of Fig. 10 and the discussion in Section 5 label z = 4/3 as the pre-asymptotic universal law and z = 1 + sigma as the BR asymptotic law; the text and caption should be made consistent.","section":"Section 5, Fig. 10"},{"comment":"The manuscript is referred to as a 'review' in Section 1 and Section 6, but it presents original numerical results; please adjust the wording to avoid confusion.","section":"Sections 1 and 6"},{"comment":"The limitation stated in Section 6---that for sigma < 1 in 2D whether true logarithmic growth sets in at larger length scales up to R ~ 500 remains an open question---is an important caveat and should also be reflected in the abstract, which currently states only that the 2D dynamics is 'more complex.'","section":"Section 6"},{"comment":"No error bars are given for R(t) or zeff(t) in any figure; given the small number of disorder realizations in 2D, a brief statement of the statistical uncertainty would help the reader judge the collapse quality.","section":"Sections 3-5, Figs. 3-15"}],"recommendation":"major_revision","confidential_remarks":"The 1D section is largely a recap of the authors' earlier PR E paper, so the 2D section carries the novelty of this manuscript. I would ask the editor to treat the 2D sigma = 3 logarithmic-growth claim as the decisive point and to require the requested direct fits and error analysis before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a mostly honest 2D extension of the authors' 1D study. The new part is the 2D numerics; the 1D section is a recap of Ref. [39]. What it does well: it treats the long-range interaction properly (Ewald summation), checks the pure LRIM limits, and it states its own limitations clearly in the summary. The citation pattern is fair; the references to the phase-transition literature are appropriate.\n\nThe central 2D claim is that at sigma=3 and Delta<=T the system crosses to logarithmic growth, with barrier exponent psi~1.23, while for sigma<1 disorder is suppressed up to R~100. The first claim is plausible but not secure. The evidence is a scaling collapse of zeff-zbar against R/ell(Delta), with ell(Delta) chosen separately for each disorder to force overlap. In the sigma=3 case the collapsed data only reach zeff-zbar~2, with zbar=2, so the power-law fit sits mostly in the crossover regime. No error bars are given, and the run count is 25. The stress-test concern that the same collapse can accommodate non-logarithmic growth over this range is reasonable. So I would treat psi~1.23 as a working estimate, not a measured exponent. The 1D exponents are on firmer ground; they reach a longer activated asymptotic range and were already published.\n\nFor sigma<1, the paper explicitly says the long-time behavior is open, and the observed disorder insensitivity is only up to R<=100. That is a fair, honest statement, not a hidden weakness.\n\nThe 'dynamical freezing' for Delta>T is a suggestion motivated by a steep rise in zeff and a failed collapse. Fine as a proposal.\n\nNet: this is a solid, clear simulation paper that fills an empty corner of the phase-ordering map. Its main quantitative conclusion needs more evidence. A serious referee should be able to push for error bars, more independent runs, and a direct test of R~(ln t)^alpha rather than relying only on the collapse. I would send it to review. I would cite it as the first 2D study.","headline":"Useful first 2D map of disorder+long-range coarsening, but the headline logarithmic-growth exponent rests on a collapse with a free length and a short scaling range.","tokens_in":19304,"tokens_out":2943,"would_cite":true,"duration_ms":34085,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Long-range interactions do not rescue power-law domain growth in disordered Ising magnets: growth stays logarithmic in time, with a reduced exponent.","keywords":["long-range Ising model","random fields","quenched disorder","domain growth","coarsening","activated dynamics","logarithmic growth","dynamical freezing"],"falsifier":"Simulate the two-dimensional RFLRIM at $T=0.1$, $\\Delta=0.1$, and $\\sigma=3$ on lattices large enough that $R(t)>500$; if the scaled effective exponent $z_{\\mathrm{eff}}-2$ departs from $a(R/\\ell)^\\psi$ with $\\psi\\simeq 1.23$, or if $R(t)$ instead fits a power law over two decades, the claimed asymptotic logarithmic growth is falsified.","tokens_in":18248,"feed_emoji":"🧲","tokens_out":7882,"duration_ms":81656,"temperature":0.7,"pith_summary":"This paper asks whether quenched random fields still force logarithmic domain growth in an Ising ferromagnet whose interactions decay as $J(r)\\sim r^{-(D+\\sigma)}$, instead of the usual power-law coarsening. The authors argue that in one dimension the answer is yes for every $\\sigma>0$: domains grow as $R(t)\\sim(\\ln t)^{\\alpha(\\sigma)}$, and the measured exponents $\\alpha(0.5)=1.31(5)$, $\\alpha(0.9)=1.17(1)$, and $\\alpha(1.5)=1.26(1)$ are all below the nearest-neighbor value $\\alpha=2$. In two dimensions they identify a crossover governed by $\\sigma$: for weak disorder ($\\Delta\\le T$) and $\\sigma=3$, a scaling collapse of the effective exponent gives a barrier exponent $\\psi\\simeq 1.23$ and confirms logarithmic growth, whereas for $\\sigma<1$ long-range interactions suppress disorder effects up to $R\\simeq 100$. For strong disorder ($\\Delta>T$) the dynamics becomes extremely slow and shows signs of dynamical freezing. The interest is that long-range drift accelerates early growth but does not restore power-law coarsening; it only changes the logarithmic-growth exponent.","feed_headline":"Long-range disorder still means logarithmic domain growth","feed_subtitle":"In 1D exponents drop below the nearest-neighbor value; in 2D weak disorder is beaten up to R=100.","key_machinery":"The load-bearing object is the disorder-barrier scaling ansatz used to identify logarithmic growth: in the activated regime the effective dynamic exponent satisfies $z_{\\mathrm{eff}}-\\bar z = a[R(t)/\\ell(\\Delta)]^{\\psi(\\sigma)}$, where $\\bar z$ is the pre-asymptotic power-law exponent of the pure long-range model, $\\ell(\\Delta)$ is a disorder-dependent crossover length adjusted to collapse data for different $\\Delta$, and $\\psi$ is the barrier exponent controlling energy barriers $E_B\\sim\\Delta R^{\\psi}$. A successful collapse under this form implies $R(t)\\sim(\\ln t)^{1/\\psi}$ and converts the upward drift of $z_{\\mathrm{eff}}(t)$ into a quantitative growth exponent. The reference values of $\\bar z$ come from the Bray-Rutenberg laws and the pure long-range Ising model: $\\bar z=1+\\sigma$ for $\\sigma<1$, $\\bar z=2$ for $\\sigma>1$, plus the $z=4/3$ zero-temperature regime in $D=2$. The diagnostic power of the method is precisely what distinguishes logarithmic growth from a plateau or freezing: logarithmic growth gives the power-law collapse, while the strong-disorder data resist any such collapse.","core_discovery":"In the random-field long-range Ising model, $H=-\\sum_{j<i} r_{ij}^{-(D+\\sigma)}s_i s_j - \\sum_i h_i s_i$ with Gaussian random fields of width $\\Delta$, quenched to low temperature, the asymptotic domain-growth law remains the activated logarithmic form $R(t)\\sim(\\ln(t/\\tau))^{\\alpha(\\sigma)}$ rather than a power law. The paper's new quantitative finding in $D=2$ is that for $\\Delta\\le T$ and $\\sigma=3$ the effective exponent obeys $z_{\\mathrm{eff}}-\\bar z = a(R/\\ell(\\Delta))^\\psi$ with $\\psi\\simeq 1.23$, giving a clean data collapse and hence logarithmic growth, while the same analysis fails for $\\Delta>T$, where the sharp rise of $z_{\\mathrm{eff}}$ with $R$ suggests dynamical freezing. In $D=1$ the paper reaffirms, following its earlier study, that logarithmic growth holds for all $\\sigma>0$ with $\\alpha(\\sigma)<2$, so long-range interactions reduce the efficiency of activated coarsening relative to the nearest-neighbor case. In both dimensions the equal-time correlation function collapses onto a disorder-independent, superuniversal scaling function. The paper's overall claim is that the Huse-Henley activated mechanism survives long-range drift, but with a $\\sigma$-dependent growth exponent and with a strong-disorder regime that may be dynamically frozen.","pith_inferences":["One consequence the paper leaves implicit: if the two-dimensional $\\psi\\simeq 1.23$ result is asymptotic, then long-range interactions make activated growth faster in exponent ($\\alpha=1/1.23\\simeq 0.81$) than the nearest-neighbor random-field value ($\\alpha\\simeq 1/1.5$), opposite to the trend reported in one dimension.","The failure to collapse the strong-disorder data cannot by itself distinguish true freezing from logarithmic growth with a very long crossover; a direct measurement of the disorder-induced barrier-height distribution, or simulations reaching $R(t)\\gg\\ell$, would decide between those readings.","A testable consequence of the scaling ansatz is that two-time quantities such as the autocorrelation function should age with $\\ln t$ rather than $t$ scaling, using the same barrier exponent; measuring them would independently confirm the activated mechanism.","The crossover length $\\ell(\\Delta)$ is treated as a fitting parameter; a theory predicting its dependence on $\\Delta$, $\\sigma$, and $T$ from the barrier distribution would turn this collapse method into a predictive scheme."],"forward_implications":["In one dimension, no matter how long-ranged the interactions are ($\\sigma>0$), quenched disorder wins asymptotically: coarsening is logarithmic, though the exponent $\\alpha(\\sigma)$ lies below the nearest-neighbor value $2$.","In two dimensions, once $\\sigma$ is large enough (here $\\sigma=3$), the same activated logarithmic regime becomes visible on accessible scales, with barrier exponent $\\psi\\simeq 1.23$, so the nearest-neighbor random-field phenomenology survives as a limit.","Small-$\\sigma$ long-range coupling protects power-law growth against weak disorder up to $R\\simeq 100$ in $L=2048$ systems; whether logarithmic growth eventually takes over beyond that scale is left open.","For disorder stronger than temperature ($\\Delta>T$) across all studied $\\sigma$, growth becomes extremely slow with no scaling collapse, and the paper interprets this as dynamical freezing rather than logarithmic coarsening.","Superuniversality holds: the scaled correlation function is independent of $\\Delta$ for all $\\sigma>0$ studied, so disorder affects only the rate of growth, not the morphology of domains."],"supporting_citations":[{"why":"Supplies the Huse-Henley activated-dynamics picture in which disorder-induced barriers force logarithmic growth, the scenario the paper tests with long-range interactions.","marker":"[7]"},{"why":"Provides the scaling analysis of the effective exponent, with data collapse through a disorder-dependent length, from which the paper extracts $\\psi$ and infers logarithmic growth.","marker":"[30, 57, 58]"},{"why":"The authors' earlier one-dimensional RFLRIM study whose results for logarithmic growth and $\\alpha(\\sigma)$ are recapitulated and extended here.","marker":"[39]"},{"why":"Gives the pure one-dimensional long-range Ising growth regimes that define the pre-asymptotic exponent $\\bar z$ used in the one-dimensional collapse.","marker":"[31]"},{"why":"Supplies the pure two-dimensional long-range Ising kinetics, including the $z=4/3$ zero-temperature regime and crossovers, used as the disorder-free reference.","marker":"[35]"},{"why":"The Bray-Rutenberg predictions that set the pure-system asymptotic exponents $\\bar z=1+\\sigma$ and $\\bar z=2$ against which disorder-induced deviations are measured.","marker":"[55, 56]"}],"fun_headline_variants":["Long-range disorder: log growth persists, 2D strong freezes","Disorder's log law holds in long-range Ising, 2D weak only","1D slower, 2D freeze risk: long-range disorder dynamics","Long-range interactions don't break disorder's log growth"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The logarithmic-growth conclusion rests on assuming the scaling form $z_{\\mathrm{eff}}-\\bar z = a(R/\\ell(\\Delta))^\\psi$, with a length scale chosen freely for each disorder strength to force the data collapse, and then identifying $\\alpha=1/\\psi$; if that assumed form is not the true asymptotic behavior, the extracted exponents do not establish logarithmic growth.","fun_headline_variants_meta":{"raw":{"variants":["Long-range disorder: log growth persists, 2D strong freezes","Disorder's log law holds in long-range Ising, 2D weak only","1D slower, 2D freeze risk: long-range disorder dynamics","Long-range interactions don't break disorder's log growth"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000808,"raw_usage":{"total_tokens":3594,"prompt_tokens":1041,"completion_tokens":2553,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":657,"completion_tokens_details":{"reasoning_tokens":2475}},"tokens_in":657,"tokens_out":2553,"duration_ms":24619,"temperature":1.0,"reasoning_tokens":2475,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:17:11.350094+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the two-dimensional RFLRIM at $T=0.1$, $\\Delta=0.1$, and $\\sigma=3$ on lattices large enough that $R(t)>500$; if the scaled effective exponent $z_{\\mathrm{eff}}-2$ departs from $a(R/\\ell)^\\psi$ with $\\psi\\simeq 1.23$, or if $R(t)$ instead fits a power law over two decades, the claimed asymptotic logarithmic growth is falsified.","supporting_citations":[{"cited_title":"Huse, C.L","cited_arxiv_id":null,"evidence_quote":"Supplies the Huse-Henley activated-dynamics picture in which disorder-induced barriers force logarithmic growth, the scenario the paper tests with long-range interactions."},{"cited_title":"Agrawal, F","cited_arxiv_id":null,"evidence_quote":"The authors' earlier one-dimensional RFLRIM study whose results for logarithmic growth and $\\alpha(\\sigma)$ are recapitulated and extended here."},{"cited_title":"Corberi, E","cited_arxiv_id":null,"evidence_quote":"Gives the pure one-dimensional long-range Ising growth regimes that define the pre-asymptotic exponent $\\bar z$ used in the one-dimensional collapse."},{"cited_title":"Agrawal, F","cited_arxiv_id":null,"evidence_quote":"Supplies the pure two-dimensional long-range Ising kinetics, including the $z=4/3$ zero-temperature regime and crossovers, used as the disorder-free reference."}],"review_version":1}