Zero Temperature Hysteresis in Random Field Ising Model on Bethe Lattices: approach to mean field behavior with increasing coordination number z

TL;DR

This paper analytically investigates zero temperature hysteresis in the random field Ising model on Bethe lattices, examining how increasing coordination number z leads to behavior approaching mean field theory, and presents new results on system energy and FORC diagrams.

Contribution

It provides an analytical solution for hysteresis in the RFIM on Bethe lattices and explores the transition to mean field behavior as z increases, including new energy and FORC analysis.

Findings

Hysteresis behavior approaches mean field as z increases.

Derived analytical expressions for energy along hysteresis loops.

Presented new results on FORC diagrams and system energy.

Abstract

We consider the analytic solution of the zero temperature hysteresis in the random field Ising model on a Bethe lattice of coordination number $z$, and study how it approaches the mean field solution in the limit z-> \infty. New analytical results concerning the energy of the system along the hysteresis loop and first order reversal curves (FORC diagrams) are also presented.