On the Glauber model in a quantum representation

TL;DR

This paper reformulates the Glauber model using a quantum approach, deriving an exact transition rate that differs from traditional models, especially at low temperatures, emphasizing the role of Ising energy.

Contribution

It introduces a quantum formulation of the Glauber model with an exact transition rate expression incorporating temperature and Ising energy from the outset.

Findings

Exact transition rate derived in quantum framework

Significant differences at low temperatures compared to classical Glauber

Transition behavior governed by Ising energy rather than microscopic time scale

Abstract

The Glauber model is reconsidered based on a quantum formulation of the Master equation. Unlike the conventional approach the temperature and the Ising energy are included from the beginning by introducing a Heisenberg-like picture of the second quantized operators. This method enables us to get an exact expression for the transition rate of a single flip-process $w_i(\sigma_i)$ which is in accordance with the principle of detailed balance. The transition rate differs significantly from the conventional one due to Glauber in the low temperature regime. Here the behavior is controlled by the Ising energy and not by the microscopic time scale.