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arXiv:cond-mat/0210135 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

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

Arnab Chatterjee, Bikas K. Chakrabarti

Published Apr 21, 2003• 25 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreve.67.046113

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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.
We discuss dynamic magnetization-reversal phenomena in the Ising model under a finite-duration external magnetic field, which competes with the existing order for . The nature of the phase boundary is estimated from the mean-field (MF) equation of motion. The susceptibility and relaxation time diverge at the MF phase boundary. A Monte Carlo study also shows divergence of the relaxation time and order-parameter fluctuations at the phase boundary. The fourth-order cumulant shows two distinct behaviors. For low temperatures and pulse durations, the value of the cumulant at the crossing point for different system sizes is far less than that for the static transition in the same dimension. This suggests a new universality class for the dynamic transition. For higher temperatures and pulse durations, the transition falls in a MF-like weak-singularity universality class.
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.
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.
We report the results of mean field and the Monte Carlo study of the dynamic magnetization-reversal transition in the Ising model, brought about by the application of an external field pulse applied in opposition to the existing order before the application of the pulse. The parameters controlling the transition are the strength hp{h}_{p}hp​ and the duration $\ensuremath{\Delta}t$ of the pulse. In the mean field case, an approximate analytical expression is obtained for the phase boundary which agrees well with that obtained numerically in the small $\ensuremath{\Delta}t$ and large TTT limit. The order parameter of the transition has been identified, and is observed to vary continuously near the transition. The order parameter exponent $\ensuremath{\beta}$ was estimated both for the mean field $(\ensuremath{\beta}=1)$ and the Monte Carlo $(\ensuremath{\beta}=0.90\ifmmode\pm\else\textpm\fi{}0.02$ in two dimensions) cases. The transition shows a ``critical slowing down'' type behavior near the phase boundary with diverging relaxation time. The divergence was found to be logarithmic in the mean field case and exponential in the Monte Carlo case. The finite size scaling technique was employed to estimate the correlation length exponent $\ensuremath{\nu}$ $(=1.5\ifmmode\pm\else\textpm\fi{}0.3$ in two dimensions) in the Monte Carlo case.
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.