Exact Solution of Ising Model on a Small-World Network

TL;DR

This paper provides an exact analytical solution for the Ising model on a small-world network, revealing its mean field transition behavior and finite-size scaling properties observed in simulations.

Contribution

It introduces an exact solution for the Ising model on a small-world network, advancing understanding of phase transitions in complex systems.

Findings

Confirms mean field character of the phase transition.

Predicts finite-size scaling behavior.

Matches numerical simulation results.

Abstract

We present an exact solution of a one-dimensional Ising chain with both nearest neighbor and random long-range interactions. Not surprisingly, the solution confirms the mean field character of the transition. This solution also predicts the finite-size scaling that we observe in numerical simulations.