Exact spin-spin correlation function for the zero-temperature random-field Ising model

TL;DR

This paper derives an exact formula for the spin-spin correlation function in the zero-temperature random-field Ising model on Bethe lattices, revealing critical behavior and divergence of correlation length at the phase transition.

Contribution

It provides the first exact expression for the correlation function in this model, connecting Bethe lattice results with mean-field critical exponents.

Findings

Correlation length diverges as a power law at criticality.

Critical exponents match mean-field predictions.

Correlation function expression is valid for arbitrary coordination number.

Abstract

An exact expression for the spin-spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spin-spin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values found for a hypercubic lattice with dimension greater than the upper critical dimension.