{"id":"21e84bdb-faf8-4f32-b4e9-8cc0ef61f28e","arxiv_id":"2606.21582","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Nonreciprocal disorder at density p > p_c in a 2D Ising model produces a continuous nonequilibrium transition that remains active at T=0, with p_c(T) ≤ 1/2 from gauge invariance.","lead":"This paper studies a 2D Ising ferromagnet with randomly placed nonreciprocal bonds and finds that above a critical density these bonds sustain dynamics all the way to zero temperature. A smart generalist might read it to see how directed interactions can stop the usual freezing in disordered magnets.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Gauge-invariance bound p_c(T)≤1/2 may fail to constrain the stochastic dynamics","rationale":"The reader's weakest_assumption is precisely the load-bearing step identified above. Because the full manuscript was not supplied to the initial reader, the verdict remains UNVERDICTED; confirming or refuting the dynamical invariance of the gauge map would directly settle the central claim.","tokens_in":1583,"tokens_out":363,"duration_ms":15242,"concrete_test":"Apply the gauge transformation explicitly to the transition rates of the nonreciprocal Glauber dynamics; recompute the effective field on each site after the transformation and check whether the resulting master equation is identical to that of a reciprocal model with the same p. If the rates differ by an O(1) bias term, rerun the T=0 Monte Carlo trajectories on the gauged versus original lattices and measure whether the activity threshold shifts.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The strongest claim requires a finite p_c persisting to T=0. The paper invokes a gauge-invariance argument to obtain the upper bound p_c(T)≤1/2. This argument is typically constructed by a local spin redefinition that maps the nonreciprocal bond distribution onto an equivalent reciprocal one while preserving the partition function or ground-state degeneracy. For the stochastic (master-equation) dynamics, however, the same local gauge transformation does not necessarily leave the transition rates invariant once nonreciprocity has broken detailed balance; the transformed rates can acquire an extra bias that shifts the location of the absorbing-state transition. Consequently the bound p_c≤1/2 need not hold for the actual nonequilibrium evolution, leaving open the possibility that p_c(T)→1 as T→0.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript examines a 2D Ising ferromagnet in which a fraction p of bonds are made nonreciprocal. It reports that the model undergoes a continuous nonequilibrium phase transition at a finite critical density p_c that remains nonzero down to T=0. A gauge-invariance argument is invoked to prove the bound p_c(T) ≤ 1/2, mean-field theory is shown to reproduce the qualitative phase diagram, and numerical simulations are presented to demonstrate that the zero-temperature dynamics stays active through athermal rare-region reversals and exhibits logarithmic coarsening, in contrast to equilibrium disordered ferromagnets that freeze.","tokens_in":1742,"tokens_out":520,"duration_ms":25966,"significance":"If the central claims hold, the work establishes that quenched nonreciprocity can sustain persistent dynamics at zero temperature in an extended system, thereby preventing the T=0 freezing characteristic of reciprocal disordered magnets. The gauge-invariance bound supplies a parameter-free analytical constraint on p_c, while the mean-field treatment provides a transparent phase diagram that aligns qualitatively with the numerics. The identification of athermal rare-region effects and activated coarsening contributes concrete mechanisms to the theory of nonequilibrium absorbing-state transitions. These results are relevant to the broader study of systems with broken detailed balance.","major_comments":[{"comment":"Gauge-invariance argument (abstract and associated section): the local spin redefinition that maps the nonreciprocal bond distribution onto an equivalent reciprocal one preserves the equilibrium partition function but does not automatically preserve the transition rates of the stochastic master equation once nonreciprocity has broken detailed balance. Consequently the derived bound p_c(T) ≤ 1/2 is not guaranteed to constrain the location of the nonequilibrium absorbing-state transition, which is load-bearing for the claim that a finite p_c persists to T=0.","section":"Gauge-invariance argument"}],"minor_comments":[{"comment":"The abstract and methods description omit simulation details such as system sizes, number of disorder realizations, error-bar estimation, and data-exclusion criteria; these should be supplied to allow independent assessment of the reported p_c(T) values.","section":"Abstract / Methods"},{"comment":"Notation for the nonreciprocal coupling strength and the precise definition of the stochastic update rule (Glauber vs. Metropolis) should be stated explicitly in the model section to facilitate reproduction.","section":"Model definition"}],"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 highlighting this subtlety in the gauge-invariance argument. We address the concern directly below and will revise the manuscript to strengthen the exposition.","responses":[{"response":"The referee correctly notes that the gauge map preserves the equilibrium measure but that nonequilibrium rates require separate verification. In the model the transition rates are functions of the local fields h_i = sum_j J_{ij} s_j (with the nonreciprocal J_{ij} drawn from the quenched distribution). The local spin redefinition s'_k = -s_k on a random subset simultaneously flips the signs of all bonds attached to those sites. Because every term in h_i transforms identically under this redefinition, the entire set of local fields {h_i} is mapped onto the set of fields of the reciprocal model. Consequently the flip probabilities, which depend only on the instantaneous local fields, are identical before and after the map. The absorbing configurations and the density at which they lose stability are therefore invariant, yielding p_c(T) ≤ 1/2 for the nonequilibrium transition at any T. We will add an explicit paragraph demonstrating this invariance of the master equation in the revised manuscript.","revision_made":"yes","referee_comment":"[Gauge-invariance argument] Gauge-invariance argument (abstract and associated section): the local spin redefinition that maps the nonreciprocal bond distribution onto an equivalent reciprocal one preserves the equilibrium partition function but does not automatically preserve the transition rates of the stochastic master equation once nonreciprocity has broken detailed balance. Consequently the derived bound p_c(T) ≤ 1/2 is not guaranteed to constrain the location of the nonequilibrium absorbing-state transition, which is load-bearing for the claim that a finite p_c persists to T=0."}],"tokens_in":1294,"tokens_out":389,"duration_ms":28086,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that this paper finds a continuous nonequilibrium transition in a 2d Ising ferromagnet with random nonreciprocal bonds that persists all the way to T=0 with a finite critical density p_c. Unlike the equilibrium disordered Ising models they cite, the zero-temperature state stays active through athermal rare-region reversals and logarithmic coarsening.\n\nThe gauge-invariance argument that caps p_c(T) at 1/2 and the mean-field phase diagram are the clearest pieces of new structure. Mean-field gets the qualitative layout right, and the contrast with equilibrium cases is drawn cleanly. If the full paper backs the numerics with proper controls, that part adds concrete support.\n\nThe soft spot is the gauge bound itself. The argument works by a local spin redefinition that preserves the equilibrium measure, but the stochastic master equation does not automatically inherit the same invariance once nonreciprocity breaks detailed balance. The transformed rates can pick up an extra bias, which could shift the absorbing-state transition and let p_c(T) rise toward 1 as T drops. The abstract presents the bound as holding, yet nothing in the provided text shows an explicit check that the rates remain equivalent under the dynamics. That leaves the upper limit on p_c at low T on uncertain ground.\n\nThis is aimed at people working on nonequilibrium statistical mechanics and disordered magnets. A reader who already thinks about nonreciprocal effects or absorbing-state transitions will find the model and the mean-field comparison useful. The setup is clean enough and the claim distinct enough that it deserves referee time, even if the dynamics part of the bound needs tightening.","headline":"Nonreciprocal disorder keeps the 2d Ising model active down to T=0 at finite p_c, but the gauge bound may not carry over to the stochastic dynamics.","tokens_in":2209,"tokens_out":411,"would_cite":false,"duration_ms":29678,"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 disorder in a 2D Ising ferromagnet prevents zero-temperature freezing.","keywords":["nonreciprocal interactions","Ising model","nonequilibrium phase transition","disorder","zero-temperature dynamics","coarsening","ferromagnet"],"falsifier":"Numerical simulation of the model at T=0 for p slightly below the claimed p_c showing complete freezing into a static configuration, or observation of no activity in the long-time limit.","tokens_in":2485,"feed_emoji":"🧲","tokens_out":550,"duration_ms":21674,"temperature":0.7,"pith_summary":"The paper examines a two-dimensional Ising model where a fraction p of bonds are made nonreciprocal, meaning the interaction between spins is not symmetric. It finds that this disorder induces a continuous nonequilibrium phase transition that persists down to absolute zero temperature, with a critical density p_c that remains finite. A gauge-invariance argument shows that p_c is at most 1/2 at any temperature. At zero temperature the system does not freeze but continues to evolve through rare-region reversals and logarithmic coarsening. This contrasts with equilibrium disordered magnets that freeze at low temperatures.","feed_headline":"Nonreciprocal bonds prevent 2D magnets freezing at T=0","feed_subtitle":"A 2D Ising model with nonreciprocal disorder shows active dynamics and a continuous transition persisting to absolute zero.","key_machinery":"The 2d Ising model with a random density p of nonreciprocal bonds, whose nonreciprocity drives the nonequilibrium transition and prevents freezing.","core_discovery":"In a 2d Ising ferromagnet with randomly placed nonreciprocal bonds at density p, a continuous nonequilibrium transition occurs at a finite critical density p_c that remains positive down to T=0. The gauge-invariance argument establishes p_c(T) ≤ 1/2 for all temperatures, while mean-field theory reproduces the qualitative features of the phase diagram. The zero-temperature dynamics stays active rather than freezing, featuring athermal rare-region reversals and logarithmic activated coarsening.","pith_inferences":["Similar nonreciprocal disorder might prevent freezing in other lattice models or higher dimensions.","Experimental realizations in active matter or synthetic spin systems could test the persistence of dynamics at low temperatures.","The gauge-invariance bound may generalize to other nonequilibrium spin systems with asymmetric couplings."],"forward_implications":["The phase boundary satisfies p_c(T) ≤ 1/2 at all temperatures.","Mean-field theory gives a qualitatively accurate phase diagram.","The zero-temperature state remains dynamically active with logarithmic coarsening.","Rare regions undergo athermal reversals that sustain activity."],"fun_headline_variants":["Nonreciprocal disorder prevents 2D ferromagnet freezing at T=0","Nonreciprocal bonds keep 2D magnets unfrozen to T=0","Disorder prevents zero-T freezing in nonreciprocal 2D magnets","Nonreciprocity prevents freezing at T=0 in 2D ferromagnets"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The gauge-invariance argument that bounds the critical density p_c at or below one half continues to hold under the stochastic dynamics of the nonreciprocal model.","fun_headline_variants_meta":{"raw":{"variants":["Nonreciprocal disorder prevents 2D ferromagnet freezing at T=0","Nonreciprocal bonds keep 2D magnets unfrozen to T=0","Disorder prevents zero-T freezing in nonreciprocal 2D magnets","Nonreciprocity prevents freezing at T=0 in 2D ferromagnets"]},"model":"grok-4.3","cost_usd":0.008477,"raw_usage":{"total_tokens":3783,"prompt_tokens":569,"num_sources_used":0,"completion_tokens":82,"cost_in_usd_ticks":84774500,"prompt_tokens_details":{"text_tokens":569,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3132,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":569,"tokens_out":82,"duration_ms":24623,"temperature":1.0,"reasoning_tokens":3132,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T12:32:42.576010+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Numerical simulation of the model at T=0 for p slightly below the claimed p_c showing complete freezing into a static configuration, or observation of no activity in the long-time limit.","supporting_citations":[],"review_version":1}