Correlation functions of the One-Dimensional Random Field Ising Model at Zero Temperature

TL;DR

This paper derives an exact expression for the correlation length in the one-dimensional random field Ising model at zero temperature, revealing a discontinuous dependence on the ratio of coupling to field strength.

Contribution

It provides the first exact calculation of the correlation length for this model, highlighting a discontinuous behavior when the ratio of coupling to field is not an integer.

Findings

Correlation length is exactly computed for non-integer ratios of 2J/h.

The correlation length exhibits a discontinuous change as a function of 2J/h.

A bound on the correlation length is established for the case p=1/2.

Abstract

We consider the one-dimensional random field Ising model, where the spin-spin coupling, $J$, is ferromagnetic and the external field is chosen to be $+h$ with probability $p$ and $-h$ with probability $1-p$. At zero temperature, we calculate an exact expression for the correlation length of the quenched average of the correlation function $\langle s_0 s_n \rangle - \langle s_0 \rangle \langle s_n \rangle$ in the case that $2J/h$ is not an integer. The result is a discontinuous function of $2J/h$. When $p = {1 \over 2}$, we also place a bound on the correlation length of the quenched average of the correlation function $\langle s_0 s_n \rangle$.