Hysteresis in Random-field Ising model on a Bethe lattice with a mixed coordination number

TL;DR

This paper investigates zero-temperature hysteresis in a mixed-coordination Bethe lattice random-field Ising model, revealing critical hysteresis behavior across all fractions of site types, thus broadening understanding of non-equilibrium phase transitions.

Contribution

It extends previous models to include mixed coordination numbers, demonstrating critical hysteresis for all non-zero fractions, and employs both numerical and probabilistic methods for analysis.

Findings

Critical hysteresis exists for all c > 0.

Extension of earlier results to mixed coordination scenarios.

Provides new insights into non-equilibrium critical phenomena.

Abstract

We study zero-temperature hysteresis in the random-field Ising model on a Bethe lattice where a fraction $c$ of the sites have coordination number $z=4$ while the remaining fraction $1-c$ have $z=3$. Numerical simulations as well as probabilistic methods are used to show the existence of critical hysteresis for all values of $c > 0$. This extends earlier results for $c=0$ and $c=1$ to the entire range $0 \le c \le 1$, and provides new insight in non-equilibrium critical phenomena.