# Critical hysteresis on dilute triangular lattice

## TL;DR

This study revisits critical hysteresis in the zero-temperature random-field Ising model on a dilute triangular lattice, revealing that criticality persists at lower dilution levels than previously thought, contrasting with Bethe lattice results.

## Contribution

The paper provides new numerical evidence showing critical hysteresis persists below one-third dilution on a triangular lattice, challenging earlier findings and highlighting differences from Bethe lattice behavior.

## Key findings

- Critical hysteresis nearly vanishes below two-thirds sublattice occupation.
- Hysteresis behavior on dilute periodic lattices differs from that on dilute Bethe lattices.
- Criticality persists at lower dilution levels than previously reported.

## Abstract

Critical hysteresis in the zero-temperature random-field Ising model on a two-dimensional triangular lattice has been studied earlier with site dilution on one sublattice. It was reported that criticality vanishes if less than one third of the sublattice is occupied. This appears at variance with recently obtained exact solutions of the model on dilute Bethe lattices and prompts us to revisit the problem using an alternate numerical method. Contrary to our speculation that criticality may not be exactly zero below one third dilution, the present study indicates it is nearly zero if approximately less than two-thirds of the sublattice is occupied. This suggests that hysteresis on dilute periodic lattices is qualitatively different from that on dilute Bethe lattices. Possible reasons are discussed briefly.