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arXiv:0706.3629 · Physical Review E

Critical fluctuations of time-dependent magnetization in a random-field Ising model

Hiroki Ohta, Shin‐ichi Sasa

Published Feb 21, 2008• 2 citations
arXivHTMLPDF

Abstract

Cooperative behaviors near the disorder-induced critical point in a random-field Ising model are numerically investigated by analyzing time-dependent magnetization in ordering processes from a special initial condition. We find that the intensity of fluctuations of time-dependent magnetization, chi(t) , attains a maximum value at a time t=tau in a normal phase and that chi(tau) and tau exhibit divergences near the disorder-induced critical point. Furthermore, spin configurations around the time tau are characterized by a length scale, which also exhibits a divergence near the critical point. We estimate the critical exponents that characterize these power-law divergences by using a finite-size scaling method.

DOI
10.1103/physreve.77.021119

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Cooperative behaviors near the disorder-induced critical point in a random-field Ising model are numerically investigated by analyzing time-dependent magnetization in ordering processes from a special initial condition. We find that the intensity of fluctuations of time-dependent magnetization, chi(t) , attains a maximum value at a time t=tau in a normal phase and that chi(tau) and tau exhibit divergences near the disorder-induced critical point. Furthermore, spin configurations around the time tau are characterized by a length scale, which also exhibits a divergence near the critical point. We estimate the critical exponents that characterize these power-law divergences by using a finite-size scaling method.
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Based on the phenomenological approach, loci of relaxation time and magnetic dispersion maxima near the critical regime in a spin-1/2 mean-field Ising model were performed. The shift in temperature (T) of relaxation time (τ) maximum was detected and its behavior near the second-order transition points are presented at different magnetic field values (h) and different lattice coordination numbers (q). An expression for the dynamic (or complex) susceptibility (χ = χ1 - iχ2) is also derived. The temperature dependence of the magnetic dispersion (χ1) and magnetic absorption (χ2) factors have been studied near the critical regime. It is found that the maximum of χ1 as a function of frequency (ω) and kinetic coefficient (L) obeying an approximately exponential increases and decreases in T- ω and T-L planes near the critical region.