Analysis of the long-range random field quantum antiferromagnetic Ising model

TL;DR

This paper introduces an exactly solvable quantum antiferromagnetic Ising model with infinite-range interactions, random fields, and frustration, analyzing its critical phenomena analytically.

Contribution

It presents a new solvable model combining randomness and frustration in quantum antiferromagnets, providing analytical insights into its critical behavior.

Findings

Identification of critical phenomena in the model

Analytical results on the effects of frustration and randomness

Insights into the spin-configuration space structure

Abstract

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions with random fields on each site, following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many-valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.