Thermodynamics of spin systems on small-world hypergraphs

TL;DR

This paper investigates the thermodynamic behavior of spin systems on small-world hypergraphs, combining analytical and numerical methods to explore phase transitions and validate findings with simulations.

Contribution

It introduces a novel analytical approach to study spin systems on small-world hypergraphs with p-spin interactions, including solutions for finite and large connectivity cases.

Findings

Analytical solutions for large connectivity cases.

Identification of ferromagnetic-paramagnetic transition points.

Validation of theoretical results with Monte-Carlo simulations.

Abstract

We study the thermodynamic properties of spin systems on small-world hypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin interactions onto a one-dimensional Ising chain with nearest-neighbor interactions. We use replica-symmetric transfer-matrix techniques to derive a set of fixed-point equations describing the relevant order parameters and free energy, and solve them employing population dynamics. In the special case where the number of connections per site is of the order of the system size we are able to solve the model analytically. In the more general case where the number of connections is finite we determine the static and dynamic ferromagnetic-paramagnetic transitions using population dynamics. The results are tested against Monte-Carlo simulations.