Quantum description of spherical spins

TL;DR

This paper introduces a quantum spherical spin model that maintains the classical model's phase transition features while providing realistic low-temperature behavior and enabling analysis of quantum phase transitions.

Contribution

A novel quantum spherical model is proposed that captures low-temperature physics and quantum phase transitions, extending the classical model's applicability.

Findings

The quantum model exhibits non-negative entropy at low temperatures.

It accurately describes quantum phase transitions in ferromagnets and spin glasses.

Crossover exponents for quantum phase transitions are provided.

Abstract

The spherical model for spins describes ferromagnetic phase transitions well, but it fails at low temperatures. A quantum version of the spherical model is proposed. It does not induce qualitative changes near the phase transition. However, it produces a physical low temperature behavior. The entropy is non-negative. Model parameters can be adapted to the description of real quantum spins. Several applications are discussed. Zero-temperature quantum phase transitions are analyzed for a ferromagnet and a spin glass in a transversal field. Their crossover exponents are presented.