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

arXiv:1008.4529 · Physical Review E

Dynamical percolation transition in the Ising model studied using a pulsed magnetic field

Soumyajyoti Biswas, Anasuya Kundu, Anjan Kumar Chandra

Published Feb 18, 2011• 24 citations
arXivHTMLPDF

Abstract

We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature and pulse width and are different from the (static) percolation transition associated with the thermal transition. For a different model that belongs to the Ising universality class, the exponents are found to be same, confirming that the behavior is a common feature of the Ising class. These observations, along with a universal critical Binder cumulant value, characterize the dynamical percolation of the Ising universality class.

DOI
10.1103/physreve.83.021109

Related papers

Dynamical percolation transition in the two-dimensional ANNNI model

Anjan Kumar Chandra

The dynamical percolation transition of the two-dimensional axial next nearest-neighbor Ising model due to a pulsed magnetic field has been studied by finite size scaling analysis (by Monte Carlo simulation) for various values of frustration parameters, pulse width and temperature (below the corresponding static transition temperature). It has been found that the size of the largest geometrical cluster shows a transition for a critical field amplitude. Although the transition points shift, the critical exponents remain invariant for a wide range of frustration parameters. They are also the same as those obtained for the 2d Ising model. This suggests that although the static phase diagrams of these two models differ significantly in various aspects, the dynamical percolation transitions of these models belong to the same universality class.

arXiv:1209.3621•Journal of Physics Condensed Matter•Mar 1, 2013•0 citations

Fluctuation cumulant behavior for the field-pulse-induced magnetization-reversal transition in Ising models

Arnab Chatterjee, Bikas K. Chakrabarti

The universality class of the dynamic magnetization-reversal transition, induced by a competing field pulse, in an Ising model on a square lattice, below its static ordering temperature, is studied here using Monte Carlo simulations. Fourth-order cumulant of the order parameter distribution is studied for different system sizes around the phase boundary region. The crossing point of the cumulant (for different system sizes) gives the transition point and the value of the cumulant at the transition point indicates the universality class of the transition. The cumulant value at the crossing point for low temperature and pulse width range is observed to be significantly less than that for the static transition in the same two-dimensional Ising model. The finite-size scaling behavior in this range also indicates a higher correlation length exponent value. For higher temperature and pulse width range, the transition seems to fall in a mean-field-like universality class.

arXiv:cond-mat/0210135•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Apr 21, 2003•25 citations

Critical droplets and phase transitions in two dimensions

Santo Fortunato

In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point ${T}_{c}$ of the thermal transition and the percolation exponents belong to a special universality class. By introducing a bond probability ${p}_{B}<1,$ the corresponding site-bond clusters keep on percolating at ${T}_{c}$ and the exponents do not change, until ${p}_{B}{=p}_{\mathrm{CK}}=1\ensuremath{-}\mathrm{exp}(\ensuremath{-}2J/kT):$ for this special expression of the bond weight the critical percolation exponents switch to the two-dimensional Ising universality class. We show here that the result is valid for a wide class of bidimensional models with a continuous magnetization transition: there is a critical bond probability ${p}_{c}$ such that, for any ${p}_{B}>~{p}_{c},$ the onset of percolation of the site-bond clusters coincides with the critical point of the thermal transition. The percolation exponents are the same for ${p}_{c}<{p}_{B}<~1$ but, for ${p}_{B}{=p}_{c},$ they suddenly change to the thermal exponents, so that the corresponding clusters are critical droplets of the phase transition. Our result is based on Monte Carlo simulations of various systems near criticality.

arXiv:cond-mat/0205211•Physical review. B, Condensed matter•Jan 15, 2003•16 citations

Universality Class of the Nonequilibrium Phase Transition in Two-Dimensional Ising Ferromagnet Driven by Propagating Magnetic Field Wave

Ajay Halder, Muktish Acharyya

The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (pinned) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth-order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes (L). From the finite size analysis of dynamic order parameter and the dynamic susceptibility , we have estimated the critical exponents and (measured from the data read at the critical temperature obtained from Binder cumulant), and (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where and ), within the limits of statistical errors.

arXiv:1805.02389•Applied Mathematics•Jan 1, 2019•0 citations

Dynamically order-disorder transition in triangular lattice driven by a time dependent magnetic field

Erol Vatansever

We have elucidated the dynamic phase transition features and finite-size scaling analysis of the triangular lattice system under the presence of a square-wave magnetic field. It has been found that as the value of half-period of the external field reaches its critical value, whose location is estimated by means of Binder cumulant, the system presents a dynamic phase transition between dynamically ordered and disordered phases. Moreover, at the dynamic phase transition point, finite-size scaling of the Monte Carlo results for the dynamic order parameter and susceptibility give the critical exponents $β/ν=0.143\pm0.004$ and $γ/ν=1.766\pm0.036$, respectively. The obtained critical exponents show that present magnetic system belongs to same universality class with the two-dimensional equilibrium Ising model.

arXiv:1706.03351•Jun 11, 2017•4 citations

Critical behavior of the geometrical spin clusters and interfaces in the two-dimensional thermalized bond Ising model

S Davatolhagh, M Moshfeghian, A A Saberi

The fractal dimensions and the percolation exponents of geometrical spin clusters of like sign at criticality are obtained numerically for an Ising model with temperature dependent annealed bond dilution, also known as the thermalized bond Ising model (TBIM), in two dimensions. For this purpose, a modified Wolff single-cluster Monte Carlo simulation is used to generate equilibrium spin configurations on square lattices in the critical region. A tie-breaking rule is employed to identify nonintersecting spin cluster boundaries along the edges of the dual lattice. The values obtained for the fractal dimensions of the spanning geometrical clusters D c , and their interfaces D I , are in perfect agreement with those reported for the standard two-dimensional ferromagnetic Ising model. Furthermore, the variance of the winding angles results in a diffusivity κ = 3 for the two-dimensional thermalized bond Ising model, thus placing it in the universality class of the regular Ising model. A finite-size scaling analysis of the largest geometrical clusters results in a reliable estimation of the critical percolation exponents for the geometrical clusters in the limit of an infinite lattice size. The percolation exponents thus obtained are also found to be consistent with those reported for the regular Ising model. These consistencies are explained in terms of the Fisher renormalization relations, which express the thermodynamic critical exponents of systems with annealed bond dilution in terms of those of the regular model system.

arXiv:1202.6683•Journal of Statistical Mechanics Theory and Experiment•Feb 21, 2012•2 citations
We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature and pulse width and are different from the (static) percolation transition associated with the thermal transition. For a different model that belongs to the Ising universality class, the exponents are found to be same, confirming that the behavior is a common feature of the Ising class. These observations, along with a universal critical Binder cumulant value, characterize the dynamical percolation of the Ising universality class.
The dynamical percolation transition of the two-dimensional axial next nearest-neighbor Ising model due to a pulsed magnetic field has been studied by finite size scaling analysis (by Monte Carlo simulation) for various values of frustration parameters, pulse width and temperature (below the corresponding static transition temperature). It has been found that the size of the largest geometrical cluster shows a transition for a critical field amplitude. Although the transition points shift, the critical exponents remain invariant for a wide range of frustration parameters. They are also the same as those obtained for the 2d Ising model. This suggests that although the static phase diagrams of these two models differ significantly in various aspects, the dynamical percolation transitions of these models belong to the same universality class.
The universality class of the dynamic magnetization-reversal transition, induced by a competing field pulse, in an Ising model on a square lattice, below its static ordering temperature, is studied here using Monte Carlo simulations. Fourth-order cumulant of the order parameter distribution is studied for different system sizes around the phase boundary region. The crossing point of the cumulant (for different system sizes) gives the transition point and the value of the cumulant at the transition point indicates the universality class of the transition. The cumulant value at the crossing point for low temperature and pulse width range is observed to be significantly less than that for the static transition in the same two-dimensional Ising model. The finite-size scaling behavior in this range also indicates a higher correlation length exponent value. For higher temperature and pulse width range, the transition seems to fall in a mean-field-like universality class.
In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point Tc{T}_{c}Tc​ of the thermal transition and the percolation exponents belong to a special universality class. By introducing a bond probability pB<1,{p}_{B}<1,pB​<1, the corresponding site-bond clusters keep on percolating at Tc{T}_{c}Tc​ and the exponents do not change, until ${p}_{B}{=p}_{\mathrm{CK}}=1\ensuremath{-}\mathrm{exp}(\ensuremath{-}2J/kT):$ for this special expression of the bond weight the critical percolation exponents switch to the two-dimensional Ising universality class. We show here that the result is valid for a wide class of bidimensional models with a continuous magnetization transition: there is a critical bond probability pc{p}_{c}pc​ such that, for any pB> pc,{p}_{B}>~{p}_{c},pB​> pc​, the onset of percolation of the site-bond clusters coincides with the critical point of the thermal transition. The percolation exponents are the same for pc<pB< 1{p}_{c}<{p}_{B}<~1pc​<pB​< 1 but, for pB=pc,{p}_{B}{=p}_{c},pB​=pc​, they suddenly change to the thermal exponents, so that the corresponding clusters are critical droplets of the phase transition. Our result is based on Monte Carlo simulations of various systems near criticality.
The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (pinned) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth-order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes (L). From the finite size analysis of dynamic order parameter and the dynamic susceptibility , we have estimated the critical exponents and (measured from the data read at the critical temperature obtained from Binder cumulant), and (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where and ), within the limits of statistical errors.
We have elucidated the dynamic phase transition features and finite-size scaling analysis of the triangular lattice system under the presence of a square-wave magnetic field. It has been found that as the value of half-period of the external field reaches its critical value, whose location is estimated by means of Binder cumulant, the system presents a dynamic phase transition between dynamically ordered and disordered phases. Moreover, at the dynamic phase transition point, finite-size scaling of the Monte Carlo results for the dynamic order parameter and susceptibility give the critical exponents β/ν=0.143±0.004β/ν=0.143\pm0.004β/ν=0.143±0.004 and γ/ν=1.766±0.036γ/ν=1.766\pm0.036γ/ν=1.766±0.036, respectively. The obtained critical exponents show that present magnetic system belongs to same universality class with the two-dimensional equilibrium Ising model.
The fractal dimensions and the percolation exponents of geometrical spin clusters of like sign at criticality are obtained numerically for an Ising model with temperature dependent annealed bond dilution, also known as the thermalized bond Ising model (TBIM), in two dimensions. For this purpose, a modified Wolff single-cluster Monte Carlo simulation is used to generate equilibrium spin configurations on square lattices in the critical region. A tie-breaking rule is employed to identify nonintersecting spin cluster boundaries along the edges of the dual lattice. The values obtained for the fractal dimensions of the spanning geometrical clusters D c , and their interfaces D I , are in perfect agreement with those reported for the standard two-dimensional ferromagnetic Ising model. Furthermore, the variance of the winding angles results in a diffusivity κ = 3 for the two-dimensional thermalized bond Ising model, thus placing it in the universality class of the regular Ising model. A finite-size scaling analysis of the largest geometrical clusters results in a reliable estimation of the critical percolation exponents for the geometrical clusters in the limit of an infinite lattice size. The percolation exponents thus obtained are also found to be consistent with those reported for the regular Ising model. These consistencies are explained in terms of the Fisher renormalization relations, which express the thermodynamic critical exponents of systems with annealed bond dilution in terms of those of the regular model system.