Exact mean-field solution of a spin chain with short-range and long-range interactions

TL;DR

This paper demonstrates that a mean-field approach becomes exact for a 1D transverse field Ising model with both short-range and long-range interactions, revealing unique phase transition behaviors including inverse melting.

Contribution

It provides an exact mean-field solution for a 1D spin chain with mixed interactions, a result previously thought to be approximate.

Findings

Exact mean-field solution in the thermodynamic limit

Identification of a second-order phase transition at finite temperature

Observation of inverse melting phenomena

Abstract

We consider the transverse field Ising model with additional all-to-all interactions between the spins. We show that a mean-field treatment of this model becomes exact in the thermodynamic limit, despite the presence of 1D short-range interactions. This is established by looking for eigenstates as coherent states with an amplitude that varies through the Hilbert space. We study then the thermodynamics of the model and identify the different phases. Among its peculiar features, this 1D model possesses a second-order phase transition at finite temperature and exhibits inverse melting.