Frozen states and active-absorbing phase transitions of the Ising model on networks

TL;DR

This study investigates the behavior of the Ising model on various complex networks, revealing phase transitions and frozen states, with differences observed between network types in finite size effects.

Contribution

It introduces a comparative analysis of frozen states and phase transitions of the Ising model on RSF, BA, and WS networks, highlighting new phase transition phenomena.

Findings

RSF exhibits an order-disorder phase transition of mean field nature.

Frozen states are present across all network types studied.

Active-absorbing phase transitions occur at known transition points in WS and RSF networks.

Abstract

A zero temperature quench of the Ising model is known to lead to a frozen steady state on random and small world networks. We study such quenches on random scale free networks (RSF) and compare the scenario with that in the Barab\'asi-Albert network (BA) and the Watts Strogatz (WS) addition type network. While frozen states are present in all the cases, the RSF shows an order-disorder phase transition of mean field nature as in the WS model as well as the existence of two absorbing phases separated by an active phase. The WS network also shows an active-absorbing (A-A) phase transition occurring at the known order-disorder transition point. The comparison of the RSF and the BA network results show interesting difference in finite size dependence.