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

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 $|H|/J<2$.

published version

References in corpus (4)

• Metastability in Glauber dynamics in the low-temperature limit: Beyond exponential asymptotics
• Droplet Nucleation and Domain Wall Motion in a Bounded Interval
• Modulation of the nucleation rate pre-exponential in a low-temperature Ising system
• Dynamic Monte Carlo Simulations for a Square-Lattice Ising Ferromagnet with a Phonon Heat Bath

Cited by in corpus (9)

• Low-temperature nucleation in a kinetic Ising model with soft stochastic dynamics
• Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers
• Nanostructure and velocity of field-driven solid-on-solid interfaces moving under a phonon-assisted dynamic
• Transition rates for a S \ge 1 model coupled to a phonon bath
• A rejection-free Monte Carlo method for the hard-disk system
• Efficiency of Rejection-Free Methods for Dynamic Monte Carlo Studies of Off-lattice Interacting Particles
• Efficiency of Rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems
• Quantum approach to nucleation times of kinetic Ising ferromagnets
• Entropic sampling dynamics of the globally-coupled kinetic Ising model