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. E

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

Sanja Janićević, Svetislav Mijatović, Djordje Spasojević

Published Apr 19, 2017• 19 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.95.042131

Related papers

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

Djordje Spasojević, Sanja Janićević, Milan Knežević

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.

Physical Review Letters•Apr 25, 2011•70 citations

Effect of coordination number on the nonequilibrium critical point

Diana Thongjaomayum, Prabodh Shukla

We study the nonequilibrium critical point of the zero-temperature random-field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random-field Ising model belong to the same universality class. The physics of this curious result is not fully understood.

arXiv:1306.1371•Physical Review E•Oct 24, 2013•14 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

Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet

Nikolaos G. Fytas, Anastasios Malakis

We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method. In the first part of our study, we present the finite-size scaling behavior of the pure model, for which we calculate the critical amplitude of the specific heat's logarithmic expansion. For the disordered system, the numerical data and the relevant detailed finite-size scaling analysis along the lines of the two well-known scenarios-logarithmic corrections versus weak universality--strongly support the field-theoretically predicted scenario of logarithmic corrections. A particular interest is paid to the sample-to-sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality.

arXiv:1001.0867•Physical Review E•Apr 14, 2010•21 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

Nonequilibrium random-field Ising model on a diluted triangular lattice

Lobisor Kurbah, Diana Thongjaomayum, Prabodh Shukla

We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number ${z}_{\mathrm{eff}}$ in the range $3\ensuremath{\le}{z}_{\mathrm{eff}}\ensuremath{\le}6$. We find that the model supports critical behavior in the range $4<{z}_{\mathrm{eff}}\ensuremath{\le}6$, but the critical exponents are independent of ${z}_{\mathrm{eff}}$. The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.

arXiv:1501.01165•Physical Review E•Jan 16, 2015•18 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 study the nonequilibrium critical point of the zero-temperature random-field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random-field Ising model belong to the same universality class. The physics of this curious result is not fully understood.
We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method. In the first part of our study, we present the finite-size scaling behavior of the pure model, for which we calculate the critical amplitude of the specific heat's logarithmic expansion. For the disordered system, the numerical data and the relevant detailed finite-size scaling analysis along the lines of the two well-known scenarios-logarithmic corrections versus weak universality--strongly support the field-theoretically predicted scenario of logarithmic corrections. A particular interest is paid to the sample-to-sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality.
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.
We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number zeff{z}_{\mathrm{eff}}zeff​ in the range $3\ensuremath{\le}{z}_{\mathrm{eff}}\ensuremath{\le}6$. We find that the model supports critical behavior in the range $4<{z}_{\mathrm{eff}}\ensuremath{\le}6$, but the critical exponents are independent of zeff{z}_{\mathrm{eff}}zeff​. The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.