Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics

Abstract

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

A universal form of slow dynamics in zero-temperature random-field Ising model

“…The fully connected model exhibits a qualitatively different behavior from finite-dimensional systems[12,13].…”

“…Particularly, in the first step of theoretical analysis, we pay attention to the model on a random graph 1 , which is regarded as one type of Bethe lattices [14]. Thus far, several interesting results on the quasi-static properties of the model on Bethe lattices have been obtained [12,13,[15][16][17][18][19]. In this letter, by performing the bifurcation analysis of the derived equation, we determine the critical exponents characterizing singular behaviors of dynamical processes.…”

Spreadsheet analysis of stability and meta-stability of low-dimensional magnetic particles using the Ising approach

“…The main quantity guiding a given system under study is the total energy. Looking at the energy state of a given local cell, it is assumed that its local energy depends on four factors of interaction with the surrounding cells, similar to the random field Ising model [28][29][30][31]. Namely, these are: energy resulting from the cell interaction with the four nearest neighbours (1), the random energy of thermal origin (2), and the energy of an externally applied magnetic field (3).…”