Exact solution of two-dimensional (2D) Ising model with a transverse field: a low-dimensional quantum spin system

TL;DR

This paper derives an exact solution for the 2D Ising model with a transverse field by relating it to the 3D Ising model, providing insights into quantum spin systems and critical phenomena.

Contribution

It presents a novel exact solution for the ferromagnetic 2D Ising model with a transverse field through a dimensional equivalence to the 3D Ising model.

Findings

Exact solution for ferromagnetic 2D Ising with transverse field

Method applicable to antiferromagnetic cases without frustration

Insights into critical phenomena in low-dimensional quantum systems

Abstract

The exact solution of ferromagnetic two-dimensional (2D) Ising model with a transverse field, which can be used to describe the critical phenomena in low-dimensional quantum spin systems, is derived by equivalence between the ferromagnetic 2D Ising model with a transverse field and the ferromagnetic three-dimensional (3D) Ising model. The results obtained in this work can be extended to be suitable for the antiferromagnetic 2D Ising model with a transverse field in the cases without frustration.