Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Numerical Evidence for Critical Behavior of the Two-Dimensional Nonequilibrium Zero-Temperature Random Field Ising Model

Djordje Spasojević, Sanja Janićević, Milan Knežević

Published Apr 25, 2011• 70 citations
Publisher

Abstract

We give numerical evidence that the two-dimensional nonequilibrium zero-temperature random field Ising model exhibits critical behavior. Our findings are based on the results of scaling analysis and collapsing of data, obtained in extensive simulations of systems with sizes sufficiently large to clearly display the critical behavior.
DOI
10.1103/physrevlett.106.175701

Related papers

Critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model on a triangular lattice

Sanja Janićević, Svetislav Mijatović, Djordje Spasojević

We present a numerical study of the critical behavior of the nonequilibrium zero-temperature random field Ising model in two dimensions on a triangular lattice. Our findings, based on the scaling analysis and collapse of data collected in extensive simulations of systems with linear sizes up to L=65536, show that the model is in a different universality class than the same model on a quadratic lattice, which is relevant for a better understanding of model universality and the analysis of experimental data.

Physical review. E•Apr 19, 2017•19 citations

Avalanche distributions in the two-dimensional nonequilibrium zero-temperature random field Ising model

Djordje Spasojević, Sanja Janićević, Milan Knežević

We present in detail the scaling analysis and data collapse of avalanche distributions and joint distributions that characterize the recently evidenced critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model. The distributions are collected in extensive simulations of systems with linear sizes up to L=131072.

Physical Review E•Nov 17, 2011•46 citations

Fluctuations and criticality in the random-field Ising model

Panagiotis E. Theodorakis, Ioannis Georgiou, Nikolaos G. Fytas

We investigate the critical properties of the $d=3$ random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength $h$ and system sizes $\mathcal{V}=L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$, with $L\ensuremath{\le}156$. Using the sample-to-sample fluctuations of various quantities and proper finite-size scaling techniques we estimate with high accuracy the critical disorder strength ${h}_{\mathrm{c}}$ and the correlation length exponent $\ensuremath{\nu}$. Additional simulations in the area of the estimated critical-field strength and relevant scaling analysis of the bond energy suggest bounds for the specific heat critical exponent $\ensuremath{\alpha}$ and the violation of the hyperscaling exponent $\ensuremath{\theta}$. Finally, a data collapse analysis of the order parameter and disconnected susceptibility provides accurate estimates for the critical exponent ratios $\ensuremath{\beta}/\ensuremath{\nu}$ and $\overline{\ensuremath{\gamma}}/\ensuremath{\nu}$, respectively.

Physical Review E•Mar 8, 2013•11 citations

Critical disorder and critical magnetic field of the nonequilibrium athermal random-field Ising model in thin systems

Svetislav Mijatović, Dragutin Jovković, Sanja Janićević +1 more

In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder R_{c}(l) and the critical magnetic field H_{c}(l) under different boundary conditions when the system thickness l varies. We propose expressions for R_{c}(l) and H_{c}(l) as well as for the effective critical disorder R_{c}^{eff}(l,L) and effective critical magnetic field H_{c}^{eff}(l,L) playing the role of the effective critical parameters for the L×L×l lattices of finite lateral size L. We support these expressions by the scaling collapses of the magnetization and susceptibility curves obtained in extensive simulations. The collapses are achieved with the two-dimensional (2D) exponents for l below some characteristic value, providing thus a numerical evidence that the thin systems exhibit a 2D-like criticality which should be relevant for the experimental analyses of thin ferromagnetic samples.

Physical review. E•Sep 9, 2019•18 citations

Analysis of spanning avalanches in the two-dimensional nonequilibrium zero-temperature random-field Ising model

Djordje Spasojević, Sanja Janićević, Milan Knežević

We present a numerical analysis of spanning avalanches in a two-dimensional (2D) nonequilibrium zero-temperature random field Ising model. Finite-size scaling analysis, performed for distribution of the average number of spanning avalanches per single run, spanning avalanche size distribution, average size of spanning avalanche, and contribution of spanning avalanches to magnetization jump, is augmented by analysis of spanning field (i.e., field triggering spanning avalanche), which enabled us to collapse averaged magnetization curves below critical disorder. Our study, based on extensive simulations of sufficiently large systems, reveals the dominant role of subcritical 2D-spanning avalanches in model behavior below and at the critical disorder. Other types of avalanches influence finite systems, but their contribution for large systems remains small or vanish.

Physical Review E•Jan 15, 2014•34 citations

Nonequilibrium athermal random-field Ising model on hexagonal lattices

Svetislav Mijatović, Dragutin Jovković, Djordje Spasojević

We present the results of a study providing numerical evidence for the absence of critical behavior of the nonequilibrium athermal random-field Ising model in adiabatic regime on the hexagonal two-dimensional lattice. The results are obtained on the systems containing up to 32768×32768 spins and are the averages of up to 1700 runs with different random-field configurations per each value of disorder. We analyzed regular systems as well as the systems with different preset conditions to capture behavior in thermodynamic limit. The superficial insight to the avalanche propagation in this type of lattice is given as a stimulus for further research on the topic of avalanche evolution. With obtained data we may conclude that there is no critical behavior of random-field Ising model on hexagonal lattice which is a result that differs from the ones found for the square and for the triangular lattices supporting the recent conjecture that the number of nearest neighbors affects the model criticality.

Physical review. E•Mar 25, 2021•15 citations
We present a numerical study of the critical behavior of the nonequilibrium zero-temperature random field Ising model in two dimensions on a triangular lattice. Our findings, based on the scaling analysis and collapse of data collected in extensive simulations of systems with linear sizes up to L=65536, show that the model is in a different universality class than the same model on a quadratic lattice, which is relevant for a better understanding of model universality and the analysis of experimental data.
We investigate the critical properties of the d=3d=3d=3 random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength hhh and system sizes $\mathcal{V}=L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$, with $L\ensuremath{\le}156$. Using the sample-to-sample fluctuations of various quantities and proper finite-size scaling techniques we estimate with high accuracy the critical disorder strength hc{h}_{\mathrm{c}}hc​ and the correlation length exponent $\ensuremath{\nu}$. Additional simulations in the area of the estimated critical-field strength and relevant scaling analysis of the bond energy suggest bounds for the specific heat critical exponent $\ensuremath{\alpha}$ and the violation of the hyperscaling exponent $\ensuremath{\theta}$. Finally, a data collapse analysis of the order parameter and disconnected susceptibility provides accurate estimates for the critical exponent ratios $\ensuremath{\beta}/\ensuremath{\nu}$ and $\overline{\ensuremath{\gamma}}/\ensuremath{\nu}$, respectively.
In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder R_{c}(l) and the critical magnetic field H_{c}(l) under different boundary conditions when the system thickness l varies. We propose expressions for R_{c}(l) and H_{c}(l) as well as for the effective critical disorder R_{c}^{eff}(l,L) and effective critical magnetic field H_{c}^{eff}(l,L) playing the role of the effective critical parameters for the L×L×l lattices of finite lateral size L. We support these expressions by the scaling collapses of the magnetization and susceptibility curves obtained in extensive simulations. The collapses are achieved with the two-dimensional (2D) exponents for l below some characteristic value, providing thus a numerical evidence that the thin systems exhibit a 2D-like criticality which should be relevant for the experimental analyses of thin ferromagnetic samples.
We present a numerical analysis of spanning avalanches in a two-dimensional (2D) nonequilibrium zero-temperature random field Ising model. Finite-size scaling analysis, performed for distribution of the average number of spanning avalanches per single run, spanning avalanche size distribution, average size of spanning avalanche, and contribution of spanning avalanches to magnetization jump, is augmented by analysis of spanning field (i.e., field triggering spanning avalanche), which enabled us to collapse averaged magnetization curves below critical disorder. Our study, based on extensive simulations of sufficiently large systems, reveals the dominant role of subcritical 2D-spanning avalanches in model behavior below and at the critical disorder. Other types of avalanches influence finite systems, but their contribution for large systems remains small or vanish.
We present the results of a study providing numerical evidence for the absence of critical behavior of the nonequilibrium athermal random-field Ising model in adiabatic regime on the hexagonal two-dimensional lattice. The results are obtained on the systems containing up to 32768×32768 spins and are the averages of up to 1700 runs with different random-field configurations per each value of disorder. We analyzed regular systems as well as the systems with different preset conditions to capture behavior in thermodynamic limit. The superficial insight to the avalanche propagation in this type of lattice is given as a stimulus for further research on the topic of avalanche evolution. With obtained data we may conclude that there is no critical behavior of random-field Ising model on hexagonal lattice which is a result that differs from the ones found for the square and for the triangular lattices supporting the recent conjecture that the number of nearest neighbors affects the model criticality.