{"id":"2a1e3a70-d109-477f-8cb5-5b4f38829c9a","arxiv_id":"2509.07529","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"In a coupled map lattice with quenched asymmetric couplings, the absorbing transition exponents vary continuously with the fraction of asymmetric bonds, matching no known universality class.","lead":"A 1D lattice of coupled maps with random left-right asymmetric couplings shows absorbing transitions whose critical exponents change continuously with the disorder fraction. If genuine, this is a rare violation of the expected directed percolation universality class.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim rests on identifying ϵ_c(p) as a true critical point, but the paper's own Fig. 6 shows generic power laws below ϵ_c and the authors cannot collapse subcritical data or measure z for p<0.5. The chosen ϵ_c may lie inside a Griffiths phase, making the continuously varying δ an artifac","rationale":"The paper has some independent support: the hyperscaling relation β/δ = ν∥ holds for all p in Table 1, and p=0 reproduces DP exponents, giving confidence in the numerics. However, the central claim of a new universality class hinges on the identification of ϵ_c. The reader's concern is exactly the most load-bearing one. I considered alternative concerns (e.g., p-dependence as a crossover, small system sizes) but the Griffiths-phase ambiguity is more fundamental. The paper's own admission that subcritical data cannot be collapsed and that z is unmeasurable for p<0.5 makes this ambiguity unresolved. A single high-precision single-seed lifetime scaling test can distinguish. Thus the verdict remains CONDITIONAL, unchanged.","tokens_in":9739,"tokens_out":7214,"duration_ms":75986,"concrete_test":"Measure the average time τ(L) to reach the absorbing state from a single seed at the proposed ϵ_c for, say, p=0.2 and p=0.4, for system sizes L=50,100,200,400,800,1600, averaging over many disorder realizations. If τ(L) grows as a power law L^z with a constant z, the point is critical; if it grows faster than any power law (e.g., exp(c L^ψ)), the point is below criticality and the observed power-law decay is a Griffiths-phase artifact. For a cleaner distinction, also plot the local exponent -d ln m/d ln t vs t at ϵ_c; if it drifts monotonically toward zero (logarithmic decay), the power-law fit is a finite-time effective exponent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The critical exponents are extracted at ϵ_c chosen as the coupling where m(t) shows a clean power law (Sec. 2, Fig. 3). However, Fig. 6 shows that for p=0.4, m(t) decays as a power law over a range of ϵ in the absorbing phase, with δ varying continuously with ϵ. This is the signature of a Griffiths phase, not of criticality. The paper's own statements support this: off-critical scaling is only possible for ϵ>ϵ_c; subcritical data do not collapse; and z cannot be measured for p<0.5 because of ultra-slow decay (Sec. 2). If ϵ_c lies inside this generic power-law region rather than at the boundary where the true critical point sits, then the reported δ(p) is simply δ(ϵ_c(p)) inside the Griffiths region. Since δ varies with ϵ, the continuous variation with p could be an artifact of how ϵ_c is selected. No error bars are given for δ, and the selection criterion ('clean power law') is not quantified. This concern is load-bearing because the entire claim of a new universality class depends on ϵ_c being the genuine critical point.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript numerically studies a one-dimensional coupled map lattice with quenched asymmetric couplings. It claims that for p=0 the model reproduces the directed percolation (DP) universality class, while for p>0 the critical point epsilon_c and the critical exponents delta, beta, nu_parallel, and z vary continuously with p, defining a new universality class. The order parameter is the fraction of turbulent sites m(t), and the paper reports power-law decay at epsilon_c, off-critical scaling in the supercritical regime, and a range of power-law decays in the absorbing phase for p=0.4. The variation of the exponents is conjectured to be related to changes in the eigenvalue spectrum of the connectivity matrix.","tokens_in":10052,"tokens_out":6629,"duration_ms":66352,"significance":"If the central claim is correct, this is a notable example of continuously varying critical exponents in a non-equilibrium absorbing phase transition, which would go beyond the usual few universality classes. The p=0 baseline reproduces the DP exponents, which is a useful internal check, and the model is simple enough to be studied further. However, the central result rests on identifying epsilon_c(p) in a setting where the order parameter also shows generic power-law decay below the apparent critical point, and the dynamical exponent z is measured only for p=0.5. The claim that all critical exponents vary continuously with p is therefore not fully established by the present data.","major_comments":[{"comment":"The critical point epsilon_c(p) is identified as the coupling at which m(t) shows a 'clean power law' on a log-log plot. Figure 6 shows, however, that for p=0.4 the order parameter decays as a power law over a range of epsilon values in the absorbing phase, with delta varying continuously with epsilon. Thus the power-law criterion does not discriminate between a true critical point and a Griffiths-type generic power-law region. Since the reported delta(p) in Table 1 is extracted at the visually selected epsilon_c, the continuous variation of delta with p could be an artifact of selecting epsilon_c inside a subcritical region where delta already varies with epsilon at fixed p. The manuscript itself states that subcritical data do not collapse and that z cannot be obtained for p<0.5 because of ultra-slow decay, which is consistent with a Griffiths-phase scenario. The central claim requires","section":"Section 2, Figs. 3 and 6, Table 1"},{"comment":"The nu_parallel values in Table 1 are numerically close to beta/delta for every p, e.g. p=0.1: 3.67 vs 3.68; p=0.2: 2.86 vs 2.84; p=0.4: 3.71 vs 3.72. The text says 'We also expect a similar value of nu_parallel from the hyperscaling relation nu_parallel = beta/delta' and then concludes that the hyperscaling relation is valid. Because beta and delta have no reported uncertainties, this check is not independent. If nu_parallel was obtained from the off-critical collapse, the near-exact agreement is suspicious and needs explanation; if nu_parallel was instead set equal to beta/delta, then the table does not provide an independent measurement of nu_parallel. Please report the fitted values with error bars and clarify the fitting procedure.","section":"Section 2, Table 1, hyperscaling relation"},{"comment":"The dynamical exponent z is measured only for p=0.5 (z=3.90). For p=0.1-0.4, z is not measured, and the statement that z would be even larger for 0<p<0.5 is an extrapolation. The abstract and summary nevertheless claim that 'these exponents change continuously' and that all critical exponents vary. With a single value of z, the continuous variation of z with p is not supported. Either provide z for at least a few values of p<0.5, or restrict the claim to the exponents that are actually measured, namely delta, beta, and nu_parallel.","section":"Section 2, Fig. 8, Table 1"}],"minor_comments":[{"comment":"The list of epsilon_c and delta values contains a duplicated label: 'for p=0.1, epsilon_c=0.6625' should presumably be p=0.2, and the sequence skips p=0.4. Compare with Table 1, where p=0.4 has epsilon_c=0.708 or 0.709 (the text gives 0.709 in one place and 0.708 in the table).","section":"Section 2, text below Eq. (3)"},{"comment":"The caption says 'for epsilon > epsilon_c, epsilon and epsilon_c (top to bottom)' but the figure does not show the three curves in a way that makes the ordering clear. Please label each curve directly with the value of epsilon relative to epsilon_c.","section":"Fig. 3 caption"},{"comment":"The beta fits report errors, but epsilon_c and delta are quoted without errors. State the range of epsilon used for each fit and the number of data points. The same applies to the off-critical collapse in Fig. 7, where the quality of collapse is only qualitative.","section":"Figs. 5 and 7"},{"comment":"The text says Saha and Mohanty found that for q=3 and q=4 the critical exponents vary continuously, but the cited title is 'Non-reciprocal interactions preserve the universality class of Potts model'. Please reconcile the text with the cited result, or rephrase to avoid apparent contradiction.","section":"Introduction, reference [25]"},{"comment":"The spectral analysis is suggestive but speculative. State explicitly that it is not used to derive any of the critical exponents, and consider moving it to a separate discussion section.","section":"Section 2, Fig. 9"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a relevant and timely question, and the p=0 baseline is a useful check. However, the central claim of a new universality class with continuously varying exponents depends on distinguishing the true critical point from the generic power-law region in the absorbing phase, and the absence of z for p<0.5 weakens the claim. I would be willing to reconsider after a revision that provides a quantitative epsilon_c criterion, error bars on delta and epsilon_c, and either z values for p<0.5 or a restricted claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper reports that a 1D coupled map lattice with asymmetric quenched couplings undergoes an absorbing transition with critical exponents that vary continuously with the fraction p of right- versus left-biased couplings. If true, that is a clean counterexample to DP universality and worth knowing. The p=0 baseline reproduces DP exponents well (δ=0.159, β=0.253, z=1.58, ν∥=1.732), which is a good sanity check. The hyperscaling relation ν∥ = β/δ is checked and holds for p>0 to the precision given, and the supercritical off-collapse is shown. The eigenvalue-spectrum discussion is a nice speculative addition, and the literature review on continuously varying exponents is reasonable.\n\nThe soft spot is the same one the stress-test flags, and I think it is real. ϵ_c is chosen for each p as the coupling where m(t) shows a clean power law. But Fig. 6 shows that for p=0.4, a power-law decay with continuously varying δ holds over a range of ϵ in the absorbing phase. That is a textbook Griffiths-phase signature. Without an independent way to locate the true critical point—such as finite-size scaling of the quasistationary density, spreading from a single seed, or a moment-ratio crossing—the reported δ(p) may simply be δ(ϵ_c(p)) evaluated inside a Griffiths regime. The paper even admits that subcritical data do not collapse and that z is unmeasurable for p<0.5 due to ultra-slow decay, both of which are consistent with the Griffiths scenario. The absence of error bars for δ, ν∥, and z, and the fact that z is only measured at p=0.5, further weaken the claim.\n\nI want to be fair: the observation may be real, and the authors are honest about their limitations. But continuously varying exponents in a region of power-law decay below the nominal critical point is exactly what a Griffiths phase looks like, and the paper does not rule that out. The typo in the text (p=0.1 listed twice with different ϵ_c and δ) is minor but doesn't help.\n\nWho gets value from this? Researchers working on absorbing transitions, disordered systems, and CMLs. It deserves a serious referee who can ask for an independent critical-point determination and error estimates. I would not cite it yet, but I would take a second look if a revised version addresses the Griffiths concern.","headline":"A plausible but under-supported claim of continuously varying critical exponents; the central issue is whether the chosen ϵ_c is a true critical point or just a point inside a Griffiths phase.","tokens_in":10547,"tokens_out":2685,"would_cite":false,"duration_ms":29762,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["05.45.Ra","05.70.Jk","05.90.+m"],"model":"deepseek-v4-flash","headline":"A coupled map lattice with quenched asymmetric couplings shows a phase transition whose critical exponents change continuously with the disorder fraction p, instead of staying in the directed percolation class.","keywords":["coupled map lattice","absorbing phase transition","directed percolation","quenched disorder","critical exponents","universality class","asymmetric coupling","eigenvalue spectrum"],"falsifier":"Perform a seed-spreading analysis for fixed p (e.g., p=0.2 and p=0.4) on much larger lattices and longer times, and locate the absorbing transition independently from the long-time exponential decay rate or from the crossing of a cumulant. Then re-extract δ, β, and ν∥ at that independently located ε_c. If the exponents come out p-independent, or if the independently located ε_c systematically differs from the power-law-fit value and grows with p, the continuous exponent variation is a finite-window artifact.","tokens_in":9624,"feed_emoji":"🔄","tokens_out":9499,"duration_ms":100321,"temperature":0.7,"pith_summary":"The paper studies a one-dimensional lattice of coupled circle maps at the onset of spatiotemporal intermittency, a system known to sit in the directed percolation universality class. It adds quenched spatial disorder by making each directed coupling asymmetric: a fraction p of sites couple more strongly to the right neighbor, the rest more strongly to the left. For any p > 0, the transition to the absorbing laminar state still shows power-law decay of the turbulent-site fraction at a critical coupling, but the decay exponent δ, the order-parameter exponent β, and the correlation-time exponent ν∥ change continuously with p. The paper's claim is that this is a genuinely new, continuously parametrized set of critical exponents—not a known universality class, not weak universality, and not a Griffiths phase—and it suggests the eigenvalue spectrum of the random connectivity matrix carries the mechanism.","feed_headline":"At p>0, critical exponents match no known universality class","feed_subtitle":"One lattice transition no longer belongs to a fixed class; its exponents slide with the disorder fraction p.","key_machinery":"The central object is a random connectivity matrix that encodes which neighbor receives the stronger coupling. At each site, the map's output goes to neighbors with weights ε1=ε/2+0.1 and ε2=ε/2−0.1; a site is type A (stronger to the left) with probability p, otherwise type B (stronger to the right), and the assignment is frozen in time. The order parameter is m(t), the fraction of sites with x_i(t)>0.5. Critical exponents are read from the power-law decay m(t)∼t^{−δ} at the critical coupling ε_c, the steady-state scaling m(∞)∼(ε−ε_c)^β, and data-collapse off-critical/finite-size scalings that yield ν∥ and z. The paper uses the eigenvalue spectrum of the connectivity matrix as the diagnostic","core_discovery":"The central claim: frozen, randomly assigned asymmetric couplings replace the directed-percolation universality of an absorbing phase transition with a one-parameter family of critical exponents. At p=0 the model gives DP values; for p=0.1–0.5, δ runs from 0.034 to 0.158, β from 0.125 to 0.607, ν∥ from 2.47 to 3.84, and z=3.90 at p=0.5. All change continuously with p; except δ at p=0.5, none match a known class. The paper excludes a Griffiths phase (the power law is at the critical point) and weak universality (all exponents vary). It attributes the effect to the connectivity matrix's eigenvalue spectrum: elliptic at p=0, holey and spread for 0<p<0.5, real at p=0.5.","pith_inferences":["I infer that the clearest way to separate a genuinely new class from a Griffiths-like effective scaling is to measure the survival probability from a single seed at the same ε_c; if the survival exponent differs from the bulk decay exponent, the transition is not a conventional critical point.","The real-axis collapse of the eigenvalue spectrum at p=0.5 suggests a testable prediction: activity fronts should have zero mean drift at p=0.5 and drift left or right at other p; measuring front velocity as a function of p would tie the spectral change to the dynamics.","If the exponent family is real, a natural next step is to look for a p-independent master scaling function after rescaling time by the p-dependent ν∥; the authors do not attempt this, and I infer that its existence would place the model under the superuniversality umbrella rather than a wholly new class."],"forward_implications":["If correct, the directed percolation universality class is not stable against this kind of frozen, locally asymmetric coupling: a line of critical points with p-dependent exponents replaces a single class.","The measured exponents satisfy the hyperscaling relation ν∥=β/δ, so the continuously varying numbers are internally consistent critical exponents, not arbitrary fit parameters.","Matching a single exponent (δ at p=0.5) is not enough to identify the universality class; the paper's p=0.5 case has DP-like δ but z and ν∥ several times the DP values.","The generic power-law range below ε_c means that standard off-critical scaling collapses cannot be performed in the subcritical regime for p>0; analyses must be restricted to the supercritical side or use other methods.","The eigenvalue-spectrum picture suggests that the connectivity matrix's spectral structure, not the local dynamics, controls the critical behavior; spectral observables could become a diagnostic for such transitions."],"supporting_citations":[{"why":"Defines the coupled circle map model and establishes that it belongs to the directed percolation class; supplies the order parameter m(t) and the base exponents this paper compares against.","marker":"[26]"},{"why":"Reviews rare-region effects at classical, quantum, and nonequilibrium phase transitions, including the activated-scaling/Griffiths route by which disorder changes DP critical behavior; the alternative scenario this paper claims to rule out.","marker":"[3]"},{"why":"Proposes the weak universality scenario for continuously varying exponents; the paper's claim that all exponents, not just ratios, vary is defined against this.","marker":"[11]"},{"why":"Shows the one-sided contact process remains in the DP class under one-sided coupling, justifying that p=0 (fully asymmetric couplings) is still DP and framing the disorder effect.","marker":"[28]"},{"why":"Provides the non-Hermitian matrix context for why the connectivity matrix at p=0.5 can have all-real eigenvalues, supporting the spectral explanation.","marker":"[29]"},{"why":"Reports a DP-origin model with continuously varying exponents along the transition line; the closest precedent that the paper distinguishes from its own case.","marker":"[20]"}],"fun_headline_variants":["Quenched disorder slides critical exponents between universality classes","Coupled map lattice: disorder makes critical exponents drift continuously","No universality class: disorder shifts critical exponents in lattice","Asymmetric couplings spawn continuously changing critical exponents"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The whole claim rests on assigning each p the true critical coupling ε_c; if the chosen ε_c lies just below the actual transition, inside the region where generic power-law decay already appears (the paper's Fig. 6 shows this region for p=0.4), then the smoothly changing δ is an artifact of curve fitting rather than a critical exponent.","fun_headline_variants_meta":{"raw":{"variants":["Quenched disorder slides critical exponents between universality classes","Coupled map lattice: disorder makes critical exponents drift continuously","No universality class: disorder shifts critical exponents in lattice","Asymmetric couplings spawn continuously changing critical exponents"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000855,"raw_usage":{"total_tokens":3582,"prompt_tokens":804,"completion_tokens":2778,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":548,"completion_tokens_details":{"reasoning_tokens":2715}},"tokens_in":548,"tokens_out":2778,"duration_ms":21414,"temperature":1.0,"reasoning_tokens":2715,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T22:02:12.070397+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform a seed-spreading analysis for fixed p (e.g., p=0.2 and p=0.4) on much larger lattices and longer times, and locate the absorbing transition independently from the long-time exponential decay rate or from the crossing of a cumulant. Then re-extract δ, β, and ν∥ at that independently located ε_c. If the exponents come out p-independent, or if the independently located ε_c systematically differs from the power-law-fit value and grows with p, the continuous exponent variation is a finite-window artifact.","supporting_citations":[{"cited_title":"Janaki, S","cited_arxiv_id":null,"evidence_quote":"Defines the coupled circle map model and establishes that it belongs to the directed percolation class; supplies the order parameter m(t) and the base exponents this paper compares against."},{"cited_title":"Vojta, Rare region effects at classical, quantum and nonequilibrium phase transitions, J","cited_arxiv_id":null,"evidence_quote":"Reviews rare-region effects at classical, quantum, and nonequilibrium phase transitions, including the activated-scaling/Griffiths route by which disorder changes DP critical behavior; the alternative scenario this paper claims to rule out."},{"cited_title":"Suzuki, New universality of critical exponents, Prog","cited_arxiv_id":null,"evidence_quote":"Proposes the weak universality scenario for continuously varying exponents; the paper's claim that all exponents, not just ratios, vary is defined against this."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows the one-sided contact process remains in the DP class under one-sided coupling, justifying that p=0 (fully asymmetric couplings) is still DP and framing the disorder effect."},{"cited_title":"Ashida, Z","cited_arxiv_id":null,"evidence_quote":"Provides the non-Hermitian matrix context for why the connectivity matrix at p=0.5 can have all-real eigenvalues, supporting the spectral explanation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports a DP-origin model with continuously varying exponents along the transition line; the closest precedent that the paper distinguishes from its own case."}],"review_version":1}