Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?

TL;DR

This study uses Monte Carlo simulations to analyze the phase transition in the 3D random field Ising model, finding evidence for a first-order transition with specific critical exponents and scaling behaviors.

Contribution

It provides new insights into the critical behavior of the 3D RFIM, supporting a two-exponent scaling scenario and challenging the traditional first-order transition characteristics.

Findings

Correlation length exponent ν=1.1±0.2

Connected susceptibility exponent η=0.50±0.05

Disconnection susceptibility exponent ar{ta}=1.03±0.05

Abstract

In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the random fields it is found that the correlation length $\xi$ diverges with an exponent $\nu=1.1\pm0.2$ at the critical temperature and that $\chi\sim\xi^{2-\eta}$ with $\eta=0.50\pm0.05$ for the connected susceptibility and $\chi_{\rm dis}\sim\xi^{4-\bar{\eta}}$ with $\bar{\eta}=1.03\pm0.05$ for the disconnected susceptibility. Together with the amplitude ratio $A=\lim_{T\to T_c}\chi_{\rm dis}/\chi^2(h_r/T)^2$ being close to one this gives further support for a two exponent scaling scenario implying $\bar{\eta}=2\eta$. The magnetization behaves discontinuously at the transition, i.e. $\beta=0$, indicating a first order transition. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multi-peak structure that is characteristic for the phase-coexistence at first order phase transition points.