Numerical study of the transition of the four dimensional Random Field Ising Model

TL;DR

This study numerically investigates the phase transition and critical behavior of the four-dimensional Random Field Ising Model above its critical temperature, revealing a glassy phase and distinct divergence of susceptibilities.

Contribution

It provides the first detailed numerical analysis of the critical exponents and phase behavior of the 4D RFIM, highlighting the existence of a glassy phase and two independent critical exponents.

Findings

Magnetic and overlap susceptibilities diverge at different temperatures.

The critical exponents satisfy the relation a2=2a2.

Evidence of a glassy phase above the critical temperature.

Abstract

We study numerically the region above the critical temperature of the four dimensional Random Field Ising Model. Using a cluster dynamic we measure the connected and disconnected magnetic susceptibility and the connected and disconnected overlap susceptibility. We use a bimodal distribution of the field with $ h_R=0.35T $ for all temperatures and a lattice size L=16. Through a least-square fit we determine the critical exponents $ \gamma $ and $ \bar{\gamma} $. We find the magnetic susceptibility and the overlap susceptibility diverge at two different temperatures. This is coherent with the existence of a glassy phase above $ T_c $. Accordingly with other simulations we find $ \bar{\gamma}=2\gamma $. In this case we have a scaling theory with two indipendet critical exponents