Analysis of spin avalanches due to interplay of disorder and temperature

Diana Thongjaomayum; Niharika Bhuyan

arxiv: 2605.23436 · v1 · pith:MJPEAXBInew · submitted 2026-05-22 · ❄️ cond-mat.dis-nn

Analysis of spin avalanches due to interplay of disorder and temperature

Niharika Bhuyan , Diana Thongjaomayum This is my paper

Pith reviewed 2026-05-25 02:35 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn

keywords random field Ising modelavalanche size distributionpower lawdisordertemperaturetriangular latticespin avalanches

0 comments

The pith

Power-law avalanche distributions in the RFIM survive only at low temperature or small to intermediate disorder.

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

The paper studies avalanche dynamics in the random-field Ising model on triangular lattices when temperature is included, moving beyond the zero-temperature limit used in most prior work. It shows that the power-law form of the avalanche-size distribution, a signature of criticality, appears only when temperature is low or when the random-field disorder is small or intermediate in strength. Temperature and disorder strength produce comparable changes to the distribution shape, so that raising either quantity blurs the power law. Simulations employ single-spin-flip updates with a finite relaxation time to track these effects across parameter space.

Core claim

In the triangular-lattice RFIM at finite temperature, power-law statistics in avalanche sizes persist exclusively in the low-temperature regime or for small and intermediate random-field strengths; temperature and disorder exert similar influences on the distribution, causing the power law to blur as either parameter is increased.

What carries the argument

Avalanche-size distribution generated by single-spin-flip dynamics with finite relaxation time in the finite-temperature RFIM on the triangular lattice.

If this is right

Power-law avalanche statistics are confined to low temperature or small and intermediate disorder.
Increases in temperature modify the avalanche-size distribution in the same manner as increases in disorder strength.
Raising either temperature or disorder blurs the power-law regime.

Where Pith is reading between the lines

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

The similarity between temperature and disorder effects implies that an effective-disorder description might absorb thermal fluctuations in limited regimes.
Real experiments may need to reach very low temperatures to recover the power laws seen in zero-temperature simulations.
Finite relaxation time could set the scale at which the distribution departs from power-law form.

Load-bearing premise

The triangular-lattice RFIM with single-spin-flip dynamics and finite relaxation time captures the essential physics of real disordered systems near criticality.

What would settle it

Direct measurement of avalanche-size distributions in a physical disordered magnetic system at elevated temperature that continues to show a clean power law would falsify the claim that power laws survive only at low temperature.

Figures

Figures reproduced from arXiv: 2605.23436 by Diana Thongjaomayum, Niharika Bhuyan.

**Figure 2.** Figure 2: FIG. 2. Disorder-dependent evolution of remanent magneti [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Remanence magnetization vs [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Hysteresis on a 999 [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Probability distribution of avalanche sizes for a [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Temperature-dependent hysteresis behaviour in a [PITH_FULL_IMAGE:figures/full_fig_p004_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Avalanche distribution for a 999 [PITH_FULL_IMAGE:figures/full_fig_p004_8.png] view at source ↗

read the original abstract

The nonequilibrium zero-temperature Random Field Ising Model (RFIM) has been extensively studied to understand critical response and avalanches in disordered driven systems. The emergence of power-law behaviour is observed over a wide region around the critical point. These studies however, are confined to zero-temperature dynamics. We study the role of temperature, which is inevitable in real experiments, in the context of RFIM on triangular lattices. We explore the interplay of different parameters: temperature, random field strength, and relaxation time which affect the prevalence of power-law behaviour on the lattice. The results indicate that power-law survives only in the regime of low temperature or small and intermediate disorder. Variations in temperature and disorder have similar affects on the avalanche-size distribution, indicating their strong correspondence. We also discuss the process of blurring out of the power law on increasing temperature or disorder.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This extends zero-T RFIM avalanche work to finite T on triangular lattices and finds power laws survive only at low T or small/intermediate disorder with similar blurring from T and disorder, but the absence of any fitting or validation details leaves the regime boundaries unconvincing.

read the letter

The paper takes the established zero-temperature RFIM avalanche results and runs them at finite temperature on a triangular lattice. It reports that power-law avalanche size distributions hold only in the low-T or small-to-intermediate disorder window, and that increasing temperature or disorder strength produces comparable cutoffs in the distributions. The exploration of relaxation time as a third parameter is a reasonable addition for modeling real systems where dynamics are not instantaneous. That is the actual content: a parameter scan showing qualitative similarity between thermal and disorder effects on the tails. No new mechanism or analytic derivation appears. The work is competent at mapping the plane in a standard model, but the central claim about where power laws remain visible rests entirely on how the distributions are classified. The provided abstract and stress-test note give no information on exponent extraction, maximum-likelihood procedures, p-values, or direct comparison to truncated power laws or exponentials. Without those steps, the reported boundaries could easily shift under different analysis choices, and the claimed correspondence between temperature and disorder cannot be checked for robustness. The model itself uses conventional single-spin-flip dynamics, which is fine, but the lack of error bars, sample sizes, or raw distribution plots makes it impossible to judge whether the blurring is cleanly separated from finite-size or fitting artifacts. This is the kind of incremental numerical study that might interest experimental groups looking for rough guidance on when thermal effects start to matter in disordered magnets. A reader already working on avalanche statistics would get little new insight beyond the qualitative statement that both T and disorder cut off the power law. I would not cite it in its current form. It could go to peer review if the full manuscript supplies reproducible fitting protocols and checks against alternative distributions; otherwise the main result is too loosely supported to justify referee time.

Referee Report

1 major / 2 minor

Summary. The manuscript examines avalanche-size distributions in the finite-temperature Random Field Ising Model on the triangular lattice with single-spin-flip dynamics. It reports that power-law regimes in the avalanche statistics persist only for low temperature or small-to-intermediate disorder strength, that temperature and disorder produce qualitatively similar blurring/cutoff effects, and that the power-law is progressively washed out as either parameter is increased.

Significance. If the regime boundaries and the claimed T–disorder correspondence can be placed on a statistically controlled footing, the work would usefully extend the well-studied zero-temperature RFIM literature by quantifying how thermal fluctuations modify avalanche criticality in disordered systems.

major comments (1)

[Abstract, §3] Abstract and §3 (numerical methods): the central claim that power-law behavior “survives only” in the low-T or small/intermediate-disorder regime rests on the classification of distributions across parameter space, yet no quantitative procedure (MLE exponent estimation, Kolmogorov–Smirnov or likelihood-ratio tests against truncated power-laws or exponentials, p-value thresholds, or robustness checks to binning/relaxation-time cutoffs) is described. Without these, the reported boundaries and the asserted similarity between T and disorder effects cannot be verified and could shift under alternative analysis choices.

minor comments (2)

[Abstract] The abstract states that “variations in temperature and disorder have similar affects”; the word should be “effects.”
[Figure captions] Figure captions and axis labels should explicitly state the range of relaxation times explored and whether the reported distributions are for the steady state or after a fixed number of Monte Carlo steps.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. The main concern is the absence of quantitative statistical procedures for identifying power-law regimes. We address this point directly below and will strengthen the analysis in revision.

read point-by-point responses

Referee: [Abstract, §3] Abstract and §3 (numerical methods): the central claim that power-law behavior “survives only” in the low-T or small/intermediate-disorder regime rests on the classification of distributions across parameter space, yet no quantitative procedure (MLE exponent estimation, Kolmogorov–Smirnov or likelihood-ratio tests against truncated power-laws or exponentials, p-value thresholds, or robustness checks to binning/relaxation-time cutoffs) is described. Without these, the reported boundaries and the asserted similarity between T and disorder effects cannot be verified and could shift under alternative analysis choices.

Authors: We agree that the original classification relied primarily on visual inspection of log-log plots and the appearance of cutoffs, which is common in the avalanche literature but lacks the rigor requested. In the revised manuscript we will add: (i) maximum-likelihood estimation of the power-law exponent with associated uncertainties, (ii) Kolmogorov–Smirnov goodness-of-fit tests, (iii) likelihood-ratio tests comparing power-law, truncated-power-law, and exponential models, and (iv) explicit p-value thresholds together with robustness checks against binning choices and relaxation-time cutoffs. These additions will place the reported regime boundaries and the T–disorder correspondence on a statistically controlled footing. revision: yes

Circularity Check

0 steps flagged

No circularity: simulation-based parameter study is self-contained

full rationale

The manuscript reports numerical results on avalanche-size distributions in the triangular-lattice RFIM under varying temperature, disorder, and relaxation time. No analytic derivations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the provided text. Claims rest on direct comparison of simulated histograms across parameter space rather than any reduction of outputs to inputs by construction. This is the expected non-circular outcome for a pure simulation study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard RFIM Hamiltonian and the assumption that single-spin-flip Metropolis dynamics on a triangular lattice produce representative avalanche statistics; no free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption The nonequilibrium dynamics of the RFIM on a triangular lattice with finite relaxation time capture the essential avalanche physics of disordered driven systems.
Invoked when the authors state they study the model to understand critical response and avalanches.

pith-pipeline@v0.9.0 · 5676 in / 1130 out tokens · 18711 ms · 2026-05-25T02:35:49.541254+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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This similar trend is observed from Fig

Thus, we conclude that power-law behaviour exists till intermediate disorder and fails beyond σ > 6. This similar trend is observed from Fig. 5(b) when t = 500. However, with increasing t, the distribution progressively flattens. The initial power-law behaviour in t = 50 be- comes less steep, indicating a higher probability of oc- currence of larger avala...

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Roy and P

A. Roy and P. Anil Kumar, A study of barkhausen avalanche statistics through the critical disorder in a fer- romagnetic thin film: Experimental investigation and theoretical modeling, Journal of Magnetism and Mag- netic Materials 493, 165710 (2020)

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A. Babu, S. Sruthy, and D. Jaiswal-Nagar, Flux jumps, cluster distribution model and vortex phase diagram of oxygenated YBa 2Cu3−xAlxO6+δ single crystals for H ∥ ab, Scientific Reports 14, 10.1038/s41598-024-78217-5 (2024)

work page doi:10.1038/s41598-024-78217-5 2024

[1] [1]

This similar trend is observed from Fig

Thus, we conclude that power-law behaviour exists till intermediate disorder and fails beyond σ > 6. This similar trend is observed from Fig. 5(b) when t = 500. However, with increasing t, the distribution progressively flattens. The initial power-law behaviour in t = 50 be- comes less steep, indicating a higher probability of oc- currence of larger avala...

work page 2022

[2] [2]

J. Xu, D. M. Silevitch, K. A. Dahmen, and T. F. Rosen- baum, Barkhausen noise in the random field Ising magnet Nd2Fe14B, Phys. Rev. B 92, 024424 (2015)

work page 2015

[3] [3]

Bohn et al., Playing with universality classes of barkhausen avalanches, Scientific Reports 8, 11294 (2018)

F. Bohn et al., Playing with universality classes of barkhausen avalanches, Scientific Reports 8, 11294 (2018)

work page 2018

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P. A. Houle and J. P. Sethna, Acoustic emission from crumpling paper, Phys. Rev. E 54, 278 (1996)

work page 1996

[5] [5]

Meng et al., Power law relations in earthquakes from microscopic to macroscopic scales, Scientific Reports 9, 10705 (2019)

F. Meng et al., Power law relations in earthquakes from microscopic to macroscopic scales, Scientific Reports 9, 10705 (2019)

work page 2019

[6] [6]

J. P. Sethna, K. Dahmen, S. Kartha, J. A. Krumhansl, B. W. Roberts, and J. D. Shore, Hysteresis and hier- 6 archies: Dynamics of disorder-driven first-order phase transformations, Phys. Rev. Lett. 70, 3347 (1993)

work page 1993

[7] [7]

Nattermann, Theory of the random field ising model, in Spin glasses and random fields (World Scien- tific, 1998) pp

T. Nattermann, Theory of the random field ising model, in Spin glasses and random fields (World Scien- tific, 1998) pp. 277–298

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Belanger and A

D. Belanger and A. Young, The random field ising model, Journal of magnetism and magnetic materials 100, 272 (1991)

work page 1991

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Sethna, K

J. Sethna, K. Dahmen, and O. Perkovic, Random-Field Ising Models of Hysteresis. The Science of Hysteresis, The Science of Hysteresis 10.1016/B978-012480874-4/50013-0 (2004)

work page doi:10.1016/b978-012480874-4/50013-0 2004

[10] [10]

Acharyya, Zero-temperature dynamic transition in the random field ising model: a monte carlo study, Phys- ica A 252, 151 (1998)

M. Acharyya, Zero-temperature dynamic transition in the random field ising model: a monte carlo study, Phys- ica A 252, 151 (1998)

work page 1998

[11] [11]

Fishman and A

S. Fishman and A. Aharony, Random field effects in dis- ordered anisotropic antiferromagnets, Journal of Physics C 12, L729 (1979)

work page 1979

[12] [12]

P. E. Theodorakis and N. G. Fytas, Random-field Ising model: Insight from zero-temperature simulations, Condensed Matter Physics 17, 10.5488/CMP.17.43003 (2015)

work page doi:10.5488/cmp.17.43003 2015

[13] [13]

D. Dhar, P. Shukla, and J. P. Sethna, Zero-temperature hysteresis in the random-field ising model on a bethe lat- tice, Journal of Physics A 30, 5259 (1997)

work page 1997

[14] [14]

Spasojevic, S

D. Spasojevic, S. Janicevic, and M. Kneˇ zevi´ c, Analysis of spanning avalanches in the two-dimensional nonequilib- rium zero-temperature random-field ising model, Physi- cal Review E 89, 012118 (2014)

work page 2014

[15] [15]

Spasojevi´ c and S

D. Spasojevi´ c and S. Jani´ cevi´ c, Two-dimensional ferro- magnetic systems with finite driving, Chaos, Solitons & Fractals 158, 112033 (2022)

work page 2022

[16] [16]

Janicevic, D

S. Janicevic, D. Knezevic, S. Mijatovic, and D. Spaso- jevic, Scaling domains in the nonequilibrium athermal random field ising model of finite systems, Journal of Sta- tistical Mechanics Theory and Experiment 2021, 013202 (2021)

work page 2021

[17] [17]

Y. C. Zohar, S. Yochelis, K. A. Dahmen, G. Jung, and Y. Paltiel, Controlling avalanche criticality in 2 D nano arrays, Scientific Reports 3, 1845 (2013)

work page 2013

[18] [18]

Durang et al., Accessing power-law statistics under experimental constraints, Phys

X. Durang et al., Accessing power-law statistics under experimental constraints, Phys. Rev. Research 5, 013011 (2023)

work page 2023

[19] [19]

J. P. Hill et al., Magnetic x-ray scattering study of ran- dom field effects in MnZnF2, Zeitschrift f¨ ur Physik B92, 285 (1993)

work page 1993

[20] [20]

Puppin and M

E. Puppin and M. Zani, Magnetic hysteresis and barkhausen noise in thin Fe films, Journal of Physics: Condensed Matter 16, 1183 (2004)

work page 2004

[21] [21]

Bingham et al., Experimental realization of the 1D random field ising model, Phys

N. Bingham et al., Experimental realization of the 1D random field ising model, Phys. Rev. Lett. 10.48550/arXiv.2110.03596 (2021)

work page doi:10.48550/arxiv.2110.03596 2021

[22] [22]

Ettori et al., Finite-temperature avalanches in 2D dis- ordered ising models, Journal of Statistical Physics 190, 89 (2023)

F. Ettori et al., Finite-temperature avalanches in 2D dis- ordered ising models, Journal of Statistical Physics 190, 89 (2023)

work page 2023

[23] [23]

Yao and R

L. Yao and R. Jack, Thermal vestiges of avalanches in the driven random field ising model, Journal of Statis- tical Mechanics: Theory and Experiment 2023, 023303 (2023)

work page 2023

[24] [24]

Miga et al., Three-dimensional random-field ising model phase transition in SrBaNb 2O6, Physical Review B 80, 220103 (2009)

S. Miga et al., Three-dimensional random-field ising model phase transition in SrBaNb 2O6, Physical Review B 80, 220103 (2009)

work page 2009

[25] [25]

Metra et al., Temperature-dependent criticality in random 2D ising models, EPJ Plus 136, 939 (2021)

M. Metra et al., Temperature-dependent criticality in random 2D ising models, EPJ Plus 136, 939 (2021)

work page 2021

[26] [26]

Yao and R

L. Yao and R. L. Jack, Thermal vestiges of avalanches in the driven random field ising model, Journal of Statistical Mechanics , 023303

work page

[27] [27]

Skantzos and A

N. Skantzos and A. Coolen, Random field ising chains with synchronous dynamics, Journal of Physics A Gen- eral Physics 33, 10.1088/0305-4470/33/9/309 (1970)

work page doi:10.1088/0305-4470/33/9/309 1970

[28] [28]

Thongjaomayum and P

D. Thongjaomayum and P. Shukla, Equilibrium via multi-spin-flip glauber dynamics in ising model (2023), arXiv:2303.14380

work page arXiv 2023

[29] [29]

Roy and P

A. Roy and P. Anil Kumar, A study of barkhausen avalanche statistics through the critical disorder in a fer- romagnetic thin film: Experimental investigation and theoretical modeling, Journal of Magnetism and Mag- netic Materials 493, 165710 (2020)

work page 2020

[30] [30]

A. Babu, S. Sruthy, and D. Jaiswal-Nagar, Flux jumps, cluster distribution model and vortex phase diagram of oxygenated YBa 2Cu3−xAlxO6+δ single crystals for H ∥ ab, Scientific Reports 14, 10.1038/s41598-024-78217-5 (2024)

work page doi:10.1038/s41598-024-78217-5 2024