Ising model with variable spin/agent strengths

Abstract

Abstract We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures of varying degrees of complexity. This allows us explore the interplay of two types of randomness: individual strengths of spins or agents and collective connectivity between them. We solve the model for the generic case of power-law spin strength and find that, with a self-averaging free energy, it has a rich phase diagram with new universality classes. Indeed, the degree of complexity added by quenched variable spins is on a par to that added by endowing simple networks with increasingly realistic geometries. The model is suitable for investigating emergent phenomena in many-body systems in contexts where non-identicality of spins or agents plays an essential role and for exporting statistical physics concepts beyond physics.