{"id":"77e041ae-1be7-46ed-8f13-049b73d7c40c","arxiv_id":"2607.02667","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"One-way coupling of an Ising order parameter to a passive conserved density is RG-relevant below four dimensions and drives a new non-equilibrium fixed point with η ≠ η′ and exact ν = 2/(d+z−2).","lead":"A Z2 order parameter coupled one-way to a freely diffusing density flows to a new non-equilibrium critical class, not Ising. The class has a measurable split between correlation and response exponents and an exact relation linking ν and z.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the paper's own disclosed limitation on non-perturbative fixed points.","rationale":"The Reader correctly isolates the uniqueness assumption as the weakest point and correctly notes that the paper itself discloses it (Introduction, Sec. VI). The load-bearing technical results—one-loop BIM fixed point, two-loop z and ω, exact Z-relations, modified Harris criterion ruling out Ising and diluted Ising in d = 3—are derived with standard tools and are free of obvious algebraic or diagrammatic errors. Because that limitation is already priced into the ACCEPT verdict and does not invalidate the near-d = 4 structure or the all-orders stability statements, no adjustment is warranted. The concrete test simply verifies the only non-trivial higher-order calculation that lifts the one-loop marginal direction.","tokens_in":29096,"tokens_out":610,"duration_ms":7264,"concrete_test":"Independently recompute the two-loop contributions to γ_λ and γ_ψ + γ_ψ̃ at X_R = 0 from the two surviving diagrams of Fig. 2 (sunset + the new \rho-noise diagram) using the same minimal-subtraction scheme; if the resulting ω = ε^{2}/96 (24 log(4/3) − 5) and the sign of e1 = −γ*_λ disagree with Eqs. (87) and (92), the stability claim at O(ε^{2}) fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (BIM fixed point as unique IR attractor for any nonzero diffusion constant, with η ≠ η′ and exact ν = 2/(d + z − 2), plus all-orders instability of Ising and diluted-Ising in d = 3) rests on standard MSR ε-expansion plus exact Z-factor identities from density linearity and the emergent shift symmetry (Sec. V). Those identities and the resulting modified Harris criterion are internally consistent and correctly applied to known Model-A / diluted-Ising exponents. The only soft spot is precisely the one the authors and the Reader already flag: uniqueness of the attractor down to d = 3 assumes no additional non-perturbative fixed point intervenes for some 3 < d* < 4. That assumption is not proven by the present calculation, but it is not hidden, and it does not undermine the near-d = 4 structure, the FDT-violating splitting, or the exact stability criteria. No stronger internal inconsistency or missing diagram appears.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript presents a complete Martin–Siggia–Rose field theory and ε=4−d renormalization-group analysis of the Brownian Ising Model (BIM): a Z2 order parameter ψ coupled nonreciprocally to a passive conserved density ρ that breaks detailed balance. Power counting establishes dc=4; one-loop β- and γ-functions identify a new IR-stable BIM fixed point (XR*=0, uR*=ε/6, f̃R*=ε/8) distinct from Model A and quenched (diluted) Ising. Critical exponents are obtained to lowest nontrivial order, with a dedicated two-loop calculation of z, η′ and ω at XR=0. Exact all-orders Z-factor identities from density linearity and an emergent shift symmetry yield the scaling relation ν=2/(d+z−2) and a modified Harris criterion that rules out both Ising and diluted-Ising fixed points in d=3 for any nonzero diffusion constant. A defining signature is the FDT-violating splitting η≠η′ already at one loop, together with a small correction-to-scaling exponent ω≈0.020 in d=3.","tokens_in":29345,"tokens_out":854,"duration_ms":9100,"significance":"If the results hold, the paper identifies a clean, structurally robust non-equilibrium route out of Ising universality that has no equilibrium analog and is controlled by a conserved density without feedback. The exact Z-factor identities, the modified Harris criterion, and the relation ν=2/(d+z−2) are all-orders statements that go beyond the ε-expansion and immediately constrain d=3 physics using known Model-A and diluted-Ising exponents. The predicted splitting η≠η′ and the negative η are sharp, falsifiable signatures of large-scale FDT violation. Explicit Feynman rules, Z-factor expressions, and the two-loop diagrams for Γψψ̃ at XR=0 (Appendices A–B) make the calculation reproducible and provide concrete benchmarks for numerics and NPRG studies. The small ω is a useful practical warning for finite-size tests.","major_comments":[],"minor_comments":[{"comment":"In Sec. IV G and Table II the two-loop expressions for z, η′ and ω are given; a short numerical evaluation at ε=1 (already stated in the text) could be repeated in the table caption for reader convenience.","section":null},{"comment":"Fig. 4 is a qualitative sketch of the full (XR,f̃R) flow. A sentence clarifying that the crossover between quenched and BIM fixed points is not captured by the standard Callan–Symanzik scheme (as noted in Sec. IV H) would help readers who might otherwise expect a continuous trajectory on that plane.","section":null},{"comment":"The companion short paper [26] is cited for the summary of results; a single sentence in the introduction stating which results are new to the present long manuscript versus the companion would improve self-containedness.","section":null},{"comment":"Notation: the same symbol τ is used both for the reduced temperature and for timescales (τρ, τψ). A brief local reminder when the timescale ratio is introduced (Sec. II D) would avoid momentary confusion.","section":null},{"comment":"Appendix A 2 lists the one-loop Z-factor relations; a parenthetical cross-reference to the exact all-orders identities of Sec. V A would make the logical continuity clearer.","section":null}],"recommendation":"accept","confidential_remarks":"The only soft spot is the authors’ own disclosed assumption that no additional non-perturbative fixed point appears for some 3<d*<4. That limitation is stated clearly and does not undermine the near-d=4 structure, the FDT splitting, or the all-orders stability criteria. I see no reason to withhold acceptance on that ground; NPRG follow-up is the natural next step, not a prerequisite for publication of the present calculation."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a careful, complete MSR ε-expansion treatment of the Brownian Ising Model: a Z2 order parameter coupled one-way to a passive conserved density. What is actually new is the IR-stable BIM fixed point itself (distinct from Model A, Model C, and quenched diluted Ising), the one- and two-loop exponents (negative η = -ε/8, η \neq η′ already at leading order, z and ω at O(ε2)), the exact all-orders relation ν = 2/(d + z - 2), and the modified Harris criterion that rules out both Ising and diluted-Ising attractors in d = 3 for any nonzero diffusion constant.\n\nThey do the technical work properly. Power counting, Feynman rules, Z-factors, and the two-loop diagrams that survive causality at XR = 0 are written out; the quenched limit recovers the known diluted-Ising β-functions as a consistency check. The structural identities (density sector non-renormalization plus the emergent shift symmetry) are clean and give the exact β-functions that let them push stability statements beyond small ε. The FDT-violating splitting η \neq η′ is a genuine, measurable signature, not just a numerical difference in exponents. The small ω ≈ 0.02 at ε = 1 is honestly reported and correctly flagged as a practical headache for numerics.\n\nThe soft spot is exactly the one they and the stress-test note name: uniqueness of the BIM attractor down to d = 3 assumes no non-perturbative fixed point appears for some 3 < d* < 4. That is the standard ε-expansion limitation; they state it in the introduction and outlook and note that NPRG would be needed. It does not undercut the near-d = 4 structure, the exact stability criteria for the competing fixed points, or the FDT signature. No missing diagrams or internal inconsistency jumped out.\n\nThis is for people who work on non-equilibrium critical dynamics, active matter hydrodynamics, and dynamical RG. It is not a data paper; it is a calculation paper that ships explicit diagrams and all-orders identities. I would send it to referees without hesitation. Worth reading and worth citing if you touch these models.","headline":"Solid dynamical RG paper that cleanly identifies a new non-equilibrium fixed point with an observable FDT-violating signature and all-orders exact relations; the only real caveat is the usual ε-expansion uniqueness assumption the authors already flag.","tokens_in":30015,"tokens_out":636,"would_cite":true,"duration_ms":6427,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Coupling an Ising order parameter to a passive conserved density drives a new non-equilibrium critical class in which correlation and response split at large scales.","keywords":["Brownian Ising model","non-equilibrium critical phenomena","renormalization group","fluctuation-dissipation violation","conserved density","universality class","Martin-Siggia-Rose","epsilon expansion"],"falsifier":"In a large three-dimensional lattice realization of the Brownian Ising model, measure whether the equal-time correlation exponent η and the integrated-response exponent η′ stay unequal as system size grows, whether pure Ising and diluted-Ising scaling are ruled out, and whether the measured ν and z obey ν = 2/(d+z−2).","tokens_in":29928,"feed_emoji":"↻","tokens_out":1205,"duration_ms":55943,"temperature":0.7,"pith_summary":"The paper analyzes the Brownian Ising model: a Z2 order parameter whose local mass is shifted by a freely diffusing conserved density, with no feedback from the order parameter onto the density. That one-sided coupling breaks detailed balance and, under renormalization-group flow below four dimensions, is relevant. It drives the system to a new infrared fixed point, distinct from both ordinary Ising and quenched diluted-Ising criticality. At the new fixed point the density acts as effective noise that is white in time but long-range in space, producing a negative anomalous dimension for correlations and, crucially, unequal anomalous dimensions for correlation and response—an observable signature of fluctuation-dissipation violation that equilibrium fixed points cannot produce. Exact identities from the linear density dynamics and an emergent shift symmetry yield the relation ν = 2/(d+z−2) and prove that both Ising and diluted-Ising fixed points are unstable in three dimensions for any nonzero diffusion constant, so the new class is the unique large-scale attractor.","feed_headline":"Passive density drives Ising systems to a new critical class","feed_subtitle":"Correlation and response split; pure Ising and quenched disorder both fail in 3D for any diffusion","key_machinery":"Martin–Siggia–Rose field theory with an ε = 4−d expansion, closed by all-orders identities among renormalization factors that follow from the linearity of the density equation and an emergent shift symmetry; these identities fix the β-functions, give the exact relation ν = 2/(d+z−2), and produce a modified Harris criterion that rules out Ising and diluted-Ising stability in three dimensions.","core_discovery":"A passive conserved density coupled only through the mass term of a Z2 order parameter is renormalization-group relevant below four dimensions and drives the system to a new non-equilibrium fixed point (the BIM fixed point). There the correlation and response functions acquire different anomalous dimensions η ≠ η′, the density generates long-range-in-space white-in-time noise that makes η negative, and the exact scaling relation ν = 2/(d+z−2) holds. Both the pure Ising and diluted-Ising fixed points are unstable in d = 3, establishing the BIM fixed point as the unique infrared attractor for any nonzero diffusion constant.","pith_inferences":["Bistable motile-particle systems and catalyst-modulated reaction networks are natural experimental platforms in which to hunt for negative η and a correlation–response split.","Functional renormalization-group or large-scale numerical studies are the direct way to test whether an intermediate fixed point appears between three and four dimensions.","The same one-sided density coupling could generate analogous non-equilibrium classes for other order-parameter symmetries beyond Z2.","Slow crossover from mean-field or Ising-like preasymptotics may explain why some active-matter simulations still look Ising-like at currently accessible sizes."],"forward_implications":["Any three-dimensional microscopic model with BIM structure and nonzero diffusion should flow to BIM exponents rather than Ising or diluted-Ising exponents.","A measured splitting η ≠ η′ between equal-time correlations and integrated response is a direct large-scale signature of broken fluctuation-dissipation that equilibrium classes cannot produce.","The correction-to-scaling exponent is small (ω ≈ 0.02 in d = 3), so finite-size corrections decay slowly and asymptotic exponents require very large systems or careful correction accounting.","The exact relation ν = 2/(d+z−2) reduces the number of independent exponents and lets improved measurements of z fix ν at two-loop order.","The quenched (diluted-Ising) fixed point is unstable to any finite defect motility, so frozen disorder is only a transient regime."],"fun_headline_variants":["Passive density drives Ising to new nonequilibrium fixed point","BIM coupling yields η ≠ η′ and exact ν = 2/(d + z − 2)","Density-order link makes pure Ising unstable in 3D","Long-range spatial noise from density flips Ising class","BIM fixed point: unique IR attractor for any diffusion"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The claim that the BIM fixed point remains the unique attractor all the way down to three dimensions assumes that no extra fixed point appears at some intermediate dimension between three and four.","fun_headline_variants_meta":{"raw":{"variants":["Passive density drives Ising to new nonequilibrium fixed point","BIM coupling yields η ≠ η′ and exact ν = 2/(d + z − 2)","Density-order link makes pure Ising unstable in 3D","Long-range spatial noise from density flips Ising class","BIM fixed point: unique IR attractor for any diffusion"]},"model":"grok-4.5","effort":"low","cost_usd":0.004738,"raw_usage":{"total_tokens":1479,"prompt_tokens":938,"num_sources_used":0,"completion_tokens":95,"cost_in_usd_ticks":47380000,"prompt_tokens_details":{"text_tokens":938,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":446,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":938,"tokens_out":95,"duration_ms":3859,"temperature":1.0,"reasoning_tokens":446,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-12T07:50:58.002689+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"In a large three-dimensional lattice realization of the Brownian Ising model, measure whether the equal-time correlation exponent η and the integrated-response exponent η′ stay unequal as system size grows, whether pure Ising and diluted-Ising scaling are ruled out, and whether the measured ν and z obey ν = 2/(d+z−2).","supporting_citations":[],"review_version":1}