The T=0 RFIM on a Bethe lattice: correlation functions along the hysteresis loop

TL;DR

This paper derives exact correlation functions for the zero-temperature RFIM on a Bethe lattice along the hysteresis loop, revealing decay properties and potential approximations for Euclidean lattices.

Contribution

It provides exact analytical expressions for correlation functions in the RFIM on a Bethe lattice at T=0, including decay behavior and implications for Euclidean lattices.

Findings

Correlation functions decay rapidly with distance in the weak-coupling regime

Proper vertices are not limited to nearest neighbors

Analytical expressions facilitate understanding of RFIM behavior

Abstract

We consider the Gaussian random field Ising model (RFIM) on the Bethe lattice at zero temperature in the presence of a uniform external field and derive the exact expressions of the two-point spin-spin and spin-random field correlation functions along the saturation hysteresis loop. To complete the analytical description and suggest possible approximations for the RFIM on Euclidian lattices we also compute the corresponding direct correlation functions (or proper vertices) and show that they decay rapidly with the distance in the weak-coupling/large disorder regime; their range, however, is not limited to the nearest-neighbor distance.