Critical behavior of a 3-D Ising model in a random field

Abstract

A Monte Carlo method has been used to study a simple cubic Ising ferromagnet in a random quenched magnetic field. The Hamiltonian for this model is H==JΣ_(ij)σ_iσ_j−Σ_iH_iσ_i, where σ_i,σ_j=±1, J is the nearest‐neighbor interaction constant, and the field H_i=t_H is fixed at each site with t_i=±1 at random and Σt_i=0. L×L×L lattices with periodic boundary conditions have been studied for a range of H and T. As expected we find a ferromagnetic ordered state which for small H undergoes a second order phase change to the paramagnetic state with increasing temperature. A finite size scaling analysis of the preliminary data suggests that the critical exponent β is substantially smaller (β∼0.2) than the usual 3‐dim Ising value of 0.31. Results obtained for small lattices indicate that below kT/J‐2 the transition becomes first order suggesting that a tricritical point appears on the critcal field curve.