Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures

TL;DR

This study investigates the divergence of the metastable lifetime prefactor in a square-lattice Ising ferromagnet coupled to phonon baths, revealing scaling behavior near a critical magnetic field at low temperatures.

Contribution

It introduces a detailed analysis of the divergent prefactor in metastable lifetimes, incorporating phonon bath effects and demonstrating scaling collapse of simulation data.

Findings

Prefactor diverges as magnetic field approaches |H|/J=2 at low temperatures.

Scaling laws describe the behavior of the divergent prefactor.

Simulation data collapse onto master curves for different bath dimensions.

Abstract

We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to $d$-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches $|H|/J=2$ at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approaches zero under these conditions. Near $|H|/J=2$ and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for $|H|/J>2$ and one for $|H|/J<2$.