Quantum phase transitions and thermodynamic properties in highly anisotropic magnets

TL;DR

This paper investigates quantum phase transitions in anisotropic magnets using models like Ising and Heisenberg, analyzing ground-state and finite-temperature properties, and comparing theoretical results with numerical and experimental data.

Contribution

It establishes a correspondence between model parameters and the quantum phi^4 model near QPT and provides analytical results for thermodynamic properties in anisotropic magnetic systems.

Findings

Scaling analysis of ground-state properties near QPT

Analytical expressions for ordering temperature and magnetization

Comparison with numerical and experimental data

Abstract

The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models and of quantum phi^4 model is established. A scaling analysis is performed for the ground-state properties. The influence of the external longitudinal magnetic field on the ground-state properties is investigated, and the corresponding magnetic susceptibility is calculated. Finite-temperature properties are considered with the use of the scaling analysis for the effective classical model proposed by Sachdev. Analytical results for the ordering temperature and temperature dependences of the magnetization and energy gap are obtained in the case of a small ground-state moment. The forms of dependences of observable quantities on the bare splitting (or magnetic field) and renormalized splitting turn out to be different. A comparison with numerical calculations and experimental data on systems demonstrating magnetic and structural transitions (e.g., into singlet state) is performed.