Ising model with variable spin/agent strengths

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. We solve it for the generic case of power-law spin strength and find that, with a self-averaging free energy, the model has a rich phase diagram with new universality classes. Indeed, the degree of complexity added by variable spins is on a par to that added by endowing simple networks with increasingly realistic geometries. It is suitable for modeling 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.

arXiv comment7 pages, 1 figure

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• Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws
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• Emergence of the 3D diluted Ising model universality class in a mixture of two magnets
• Consensus from group interactions: An adaptive voter model on hypergraphs
• Ising model with varying spin strength on a scale-free network: scaling functions and critical amplitude ratios