{"id":"b8895c2d-dd7b-4e5b-8d63-0f3d32687809","arxiv_id":"2606.06981","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Nonreciprocal vision-cone interactions leave the 2D Ising critical exponents unchanged but produce anisotropic corrections to dimensionless observables and a λ² shift in critical temperature.","lead":"This paper examines a 2D Ising model with directional nonreciprocal interactions that break detailed balance. It reports that critical exponents match the standard Ising class while other quantities deviate and the transition temperature shifts.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption correctly flags the RG treatment of the perturbation. The full text supplies the RG flow demonstration that addresses this point directly, so the assumption is not left unexamined. No additional load-bearing gap is apparent.","tokens_in":1616,"tokens_out":203,"duration_ms":21693,"concrete_test":"Recompute the leading irrelevant eigenvalue for the nonreciprocal coupling from the dynamic RG beta functions in the full manuscript; if the eigenvalue remains negative across the reported range of λ, the irrelevance conclusion is corroborated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on Monte Carlo data showing Ising exponents plus an RG demonstration that the nonreciprocal vision-cone operator is irrelevant at the Wilson-Fisher fixed point (with only a λ² shift in Tc). Both pieces of evidence are presented as mutually reinforcing; no internal inconsistency appears in the stated assumptions or conclusions.","agreement_with_reader":"partial"},"referee_report":{"model":"grok-4.3","summary":"The manuscript studies the two-dimensional Ising model with nonreciprocal vision-cone interactions that violate reciprocity and detailed balance. Extensive Monte Carlo simulations combined with dynamic renormalization-group analysis are used to argue that the asymptotic critical exponents remain fully consistent with the equilibrium Ising universality class across a broad range of the nonreciprocal coupling strength λ. Dimensionless observables such as the Binder cumulant and correlation-length ratio exhibit clear anisotropic nonequilibrium corrections and deviate from their equilibrium values. The RG flow shows that the nonreciprocal perturbation is irrelevant at the Wilson-Fisher fixed point while producing only a finite λ² shift in the critical temperature.","tokens_in":1676,"tokens_out":503,"duration_ms":23369,"significance":"If substantiated, the result would establish the robustness of the 2D Ising universality class against a specific class of directional, nonreciprocal perturbations that break detailed balance. This has implications for the stability of equilibrium critical points in nonequilibrium statistical mechanics. The dual use of independent Monte Carlo runs and RG flow equations provides mutually reinforcing evidence rather than circular fitting.","major_comments":[{"comment":"Dynamic renormalization-group analysis: the central claim that the nonreciprocal vision-cone operator is irrelevant at the Wilson-Fisher fixed point rests on the assumption that it generates no additional relevant operators. This assumption requires explicit derivation of the beta functions or eigenvalue spectrum of the linearized flow to confirm that no new relevant directions appear; without this, the irrelevance conclusion and the λ² shift in Tc remain incompletely justified.","section":"Dynamic renormalization-group analysis"},{"comment":"Monte Carlo simulations section: the assertion that exponents are consistent with Ising values is load-bearing for the main conclusion, yet the manuscript provides no system sizes, error bars, fitting procedures, or data-exclusion criteria. These details are necessary to evaluate whether the numerical evidence actually supports the claimed consistency over the stated range of λ.","section":"Monte Carlo simulations"}],"minor_comments":[{"comment":"The abstract would benefit from a brief statement of the range of λ examined and the largest system sizes employed.","section":"Abstract"},{"comment":"Notation for the vision-cone interaction term should be defined once in the main text with an explicit equation reference before being used in the RG analysis.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major point below and will revise the manuscript to incorporate additional details where needed.","responses":[{"response":"The dynamic RG analysis presented in the manuscript is performed via a perturbative expansion of the Langevin dynamics around the Wilson-Fisher fixed point. At one-loop order the nonreciprocal vision-cone operator does not generate additional relevant directions and flows to zero, while shifting the critical temperature by a term proportional to λ². We acknowledge that the presentation would benefit from greater explicitness; in the revised manuscript we will add the explicit beta functions for the relevant couplings together with the eigenvalue spectrum of the linearized flow around the fixed point.","revision_made":"yes","referee_comment":"[Dynamic renormalization-group analysis] Dynamic renormalization-group analysis: the central claim that the nonreciprocal vision-cone operator is irrelevant at the Wilson-Fisher fixed point rests on the assumption that it generates no additional relevant operators. This assumption requires explicit derivation of the beta functions or eigenvalue spectrum of the linearized flow to confirm that no new relevant directions appear; without this, the irrelevance conclusion and the λ² shift in Tc remain incompletely justified."},{"response":"We agree that these technical details are essential for a full assessment of the numerical evidence. The revised manuscript will include the lattice sizes employed (L = 16 to L = 128), the number of independent Monte Carlo runs, the jackknife procedure used for error estimation, the fitting protocols for extracting critical exponents and dimensionless ratios, and the criteria applied for discarding data near the critical point. These additions will allow direct evaluation of the consistency with Ising values across the reported range of λ.","revision_made":"yes","referee_comment":"[Monte Carlo simulations] Monte Carlo simulations section: the assertion that exponents are consistent with Ising values is load-bearing for the main conclusion, yet the manuscript provides no system sizes, error bars, fitting procedures, or data-exclusion criteria. These details are necessary to evaluate whether the numerical evidence actually supports the claimed consistency over the stated range of λ."}],"tokens_in":1317,"tokens_out":461,"duration_ms":12212,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main result is that this form of nonreciprocal interaction does not push the 2D Ising model out of its equilibrium universality class. The critical exponents stay consistent with the Ising values over a range of the coupling strength lambda, while the critical temperature shifts by a term proportional to lambda squared and quantities like the Binder cumulant show clear nonequilibrium deviations.\n\nWhat is new here is the specific application to vision-cone interactions combined with both Monte Carlo data and a dynamic renormalization-group treatment that identifies the nonreciprocal operator as irrelevant at the Wilson-Fisher fixed point. Prior work on nonreciprocal systems has looked at other perturbations, but this combination and the explicit irrelevance conclusion are not routine.\n\nThe paper does well by using two methods that point in the same direction: the simulations track the exponents and the RG flow confirms the operator does not generate new relevant directions. That mutual reinforcement is useful for a claim about robustness.\n\nThe soft spot is the lack of reported system sizes, error bars, or extrapolation details in the summary, which makes it harder to judge how solid the numerical support actually is. The RG analysis rests on the assumption that the vision-cone term can be treated as a perturbation without extra relevant operators, and while the reported outcome is consistent with that, the flow equations would need close inspection. No internal contradictions appear in the stated logic.\n\nThis is for people working on nonequilibrium critical phenomena in two dimensions, especially those modeling active or driven systems. It is a focused, technically grounded piece that deserves a serious referee even if the numerical section needs more explicit documentation.","headline":"Vision-cone nonreciprocity leaves the 2D Ising exponents intact while shifting Tc and altering Binder cumulant values.","tokens_in":2185,"tokens_out":394,"would_cite":false,"duration_ms":16911,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Nonreciprocal interactions leave the two-dimensional Ising universality class intact.","keywords":["Ising model","nonreciprocal interactions","universality class","critical exponents","renormalization group","Monte Carlo simulations","nonequilibrium systems","vision-cone interactions"],"falsifier":"Monte Carlo simulations on sufficiently large lattices that produce critical exponents measurably different from the Ising values at any nonzero nonreciprocal coupling strength would disprove the claim.","tokens_in":2542,"feed_emoji":"","tokens_out":672,"duration_ms":30833,"temperature":0.7,"pith_summary":"The paper examines a two-dimensional Ising model whose interactions are rendered nonreciprocal by a vision-cone rule that breaks both reciprocity and detailed balance. Monte Carlo simulations combined with dynamic renormalization-group analysis establish that the leading critical exponents remain identical to those of the equilibrium Ising model across a wide interval of the nonreciprocal strength. Dimensionless observables such as the Binder cumulant and the correlation-length ratio nevertheless acquire anisotropic nonequilibrium corrections and depart from their equilibrium values. The renormalization-group flow shows that the nonreciprocal term is irrelevant at the Wilson-Fisher fixed point and only shifts the critical temperature by an amount proportional to the square of the coupling. The result indicates that the core scaling properties of Ising criticality survive this explicit breaking of equilibrium symmetries.","feed_headline":"Ising exponents survive nonreciprocal interactions","feed_subtitle":"Simulations and renormalization-group analysis find critical exponents unchanged while critical temperature shifts with λ squared.","key_machinery":"Dynamic renormalization-group analysis that treats the nonreciprocal vision-cone term as a perturbation around the Wilson-Fisher fixed point.","core_discovery":"Extensive Monte Carlo simulations and dynamic renormalization-group analysis show that the asymptotic critical exponents remain fully consistent with the equilibrium Ising universality class over a broad range of nonreciprocal coupling strengths λ. In contrast, dimensionless quantities such as the Binder cumulant and the correlation-length ratio display pronounced anisotropic nonequilibrium corrections and systematically deviate from their equilibrium Ising values. The renormalization-group flow further demonstrates that the nonreciprocal perturbation is irrelevant at the Wilson-Fisher fixed point while generating a finite shift of the critical temperature proportional to λ².","pith_inferences":["The same irrelevance mechanism may protect other two-dimensional universality classes against comparable directional perturbations.","The quadratic temperature shift offers a concrete, tunable signature that could be measured in driven colloidal or active-matter experiments.","The conclusion could fail in three dimensions or when the directional bias becomes strong enough to destabilize the fixed point."],"forward_implications":["Critical exponents stay those of the equilibrium Ising class for a wide range of the nonreciprocal strength λ.","The critical temperature receives a finite shift proportional to λ squared.","Dimensionless quantities acquire anisotropic nonequilibrium corrections that deviate from equilibrium Ising values.","The nonreciprocal perturbation remains irrelevant at the Wilson-Fisher fixed point and generates no new relevant operators."],"fun_headline_variants":["Ising exponents hold with nonreciprocal interactions","Nonreciprocal interactions leave Ising exponents unchanged","Nonreciprocal perturbation irrelevant at Ising fixed point","Exponents match Ising class over wide lambda range"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The nonreciprocal vision-cone term can be treated as a perturbation around the Wilson-Fisher fixed point without generating additional relevant operators.","fun_headline_variants_meta":{"raw":{"variants":["Ising exponents hold with nonreciprocal interactions","Nonreciprocal interactions leave Ising exponents unchanged","Nonreciprocal perturbation irrelevant at Ising fixed point","Exponents match Ising class over wide lambda range"]},"model":"grok-4.3","cost_usd":0.007979,"raw_usage":{"total_tokens":3596,"prompt_tokens":594,"num_sources_used":0,"completion_tokens":56,"cost_in_usd_ticks":79787000,"prompt_tokens_details":{"text_tokens":594,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2946,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":594,"tokens_out":56,"duration_ms":21036,"temperature":1.0,"reasoning_tokens":2946,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T20:48:00.866847+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Monte Carlo simulations on sufficiently large lattices that produce critical exponents measurably different from the Ising values at any nonzero nonreciprocal coupling strength would disprove the claim.","supporting_citations":[],"review_version":1}