Critical hysteresis on dilute triangular lattice

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.Comment: Replaced with published version (11 pages, 8 figures

Exact Expressions for Minor Hysteresis Loops in the Random Field Ising Model on a Bethe Lattice at Zero Temperature

We obtain exact expressions for the minor hysteresis loops in the ferromagnetic random field Ising model on a Bethe lattice at zero temperature in the case when the driving field is cycled infinitely slowly.Comment: Replaced with the published versio