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Nonreciprocal disorder in a 2D Ising ferromagnet prevents zero-temperature freezing.

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2026-06-26 12:32 UTC pith:JOE2A3PE

load-bearing objection 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. the 1 major comments →

arxiv 2606.21582 v1 pith:JOE2A3PE submitted 2026-06-19 cond-mat.stat-mech cond-mat.dis-nn

Nonreciprocal Disorder Prevents Zero-Temperature Freezing in a Ferromagnet

Noah Grodzinski , Robert L. Jack , Sarah A. M. Loos This is my paper
classification cond-mat.stat-mech cond-mat.dis-nn
keywords nonreciprocal interactionsIsing modelnonequilibrium phase transitiondisorderzero-temperature dynamicscoarseningferromagnet
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

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.

Core claim

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.

What carries the argument

The 2d Ising model with a random density p of nonreciprocal bonds, whose nonreciprocity drives the nonequilibrium transition and prevents freezing.

Load-bearing premise

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.

What would settle it

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.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • 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.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 2 minor

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.

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 (1)
  1. [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.
minor comments (2)
  1. [Abstract / Methods] 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.
  2. [Model definition] 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.

Simulated Author's Rebuttal

1 responses · 0 unresolved

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.

read point-by-point responses

  1. Referee: [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.

    Authors: 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: yes

Circularity Check

0 steps flagged

No circularity: gauge bound and mean-field are independent of numerics; no reductions by construction.

full rationale

The abstract and provided excerpts present a gauge-invariance argument that directly yields the bound p_c(T)≤1/2 and a separate mean-field calculation for the phase diagram. These are stated as analytical results supporting the numerical observation of a continuous transition to finite p_c at T=0. No self-citations are invoked as load-bearing, no parameters are fitted to data and then relabeled as predictions, and no ansatz or uniqueness theorem reduces the central claim to its own inputs by definition. The description of athermal rare-region reversals and logarithmic coarsening is presented as an observed dynamical feature rather than a tautological renaming. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard 2D Ising Hamiltonian plus the addition of nonreciprocal bonds at random locations; the only explicit new element is the gauge-invariance bound on p_c.

axioms (1)
  • domain assumption Gauge-invariance argument yields p_c(T) ≤ 1/2
    Invoked to bound the location of the transition for all temperatures.

pith-pipeline@v0.9.1-grok · 5636 in / 1179 out tokens · 42604 ms · 2026-06-26T12:32:42.576010+00:00 · methodology

0 comments
read the original abstract

Nonreciprocal interactions underpin diverse nonequilibrium phenomena, yet the effects of quenched nonreciprocity in extended systems remain largely unexplored. We study a $2d$ Ising model with randomly distributed nonreciprocal bonds at density $p$, finding a continuous nonequilibrium transition down to $T=0$ with finite $p_c$. A gauge-invariance argument yields $p_c(T)\leq1/2$, and mean-field theory predicts a qualitatively correct phase diagram. Unlike equilibrium disordered models, the zero-temperature dynamics remains active, with athermal rare-region reversals and logarithmic "activated" coarsening.

Figures

Figures reproduced from arXiv: 2606.21582 by Noah Grodzinski, Robert L. Jack, Sarah A. M. Loos.

Figure 1
Figure 1. Figure 1: Phases. (a) Phase diagram in the (p, T)-plane. Colours show late-time magnetisation (t = 2×105 , N = 512, initialised at m0 = 1.0; the positive m0 leads to some residual magnetisation in the disordered phase near criticality). Squares and triangles mark pc(T) extrapolated from the divergences of ξ and τ (see Supplemental Material); red curve is a fit Tc ∝ |pc − p| ϕ . Inset: mean-field magnetisation and tr… view at source ↗
Figure 2
Figure 2. Figure 2: Evidence for a continuous zero-temperature phase [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Activated coarsening in the ordered phase. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Prevented freezing by nonreciprocity. (a) Fraction [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

discussion (0)

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Forward citations

Cited by 1 Pith paper

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  1. Fluctuation-dissipation violations in mean-field non-reciprocal spin glasses

    cond-mat.stat-mech 2026-07 conditional novelty 7.0

    In the spherical SK model with non-reciprocal couplings, time-translation invariance is restored for any asymmetry, yet the steady state violates the fluctuation-dissipation theorem via an exponentially vanishing ratio.

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