Quantum phase transitions and thermodynamic properties in highly anisotropic magnets

The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse held and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models and of the 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 turnout to be different. A comparison with numerical calculations and experimental data on systems demonstrating magnetic and structural transitions (e.g., into a singlet state) is performed.