Decay of the metastable phase in d=1 and d=2 Ising models

TL;DR

This paper analytically calculates the decay rate of the metastable phase in one- and two-dimensional Ising models, revealing oscillations and lattice effects near the coexistence line at zero temperature.

Contribution

It provides a perturbative calculation of tunneling decay rates in 1D and maps results onto 2D models, confirming droplet theory predictions and identifying lattice corrections.

Findings

Decay rate $Gamma$ oscillates with magnetic field $h_z$

Droplet theory predictions are verified in the 2D Ising model

Evidence of discrete-lattice corrections in metastable free energy

Abstract

We calculate perturbatively the tunneling decay rate $\Gamma$ of the metastable phase in the quantum d=1 Ising model in a skew magnetic field near the coexistence line $0<h_{x}<1, h_{z}\to -0$ at T=0. It is shown that $\Gamma$ oscillates in the magnetic field $h_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d=2 Ising model at $T<T_c$, we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We find also evidence for the discrete-lattice corrections in this metastable phase free energy.