Random field Ising model on networks with inhomogeneous connections

TL;DR

This paper analyzes the zero-temperature phase transition of the random field Ising model on scale-free networks, revealing how network topology and field distribution shape influence the transition's nature.

Contribution

It provides an analytic mean-field theory for phase transitions in the model on scale-free networks, identifying conditions for continuous or discontinuous transitions.

Findings

Spins are always ordered for degree exponent γ<3.

Phase transition occurs for γ>3 as disorder increases.

Transition type depends on the random field distribution shape.

Abstract

We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent $\gamma$. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for $\gamma<3$. On the other hand, the spins undergo a phase transition from an ordered phase to a disordered phase as the dispersion of the random fields increases for $\gamma > 3$. The phase transition may be either continuous or discontinuous depending on the shape of the random field distribution. We derive the condition for the nature of the phase transition. Numerical simulations are performed to confirm the results.