# Generic phase coexistence in the totally asymmetric kinetic Ising model

## TL;DR

This paper investigates phase coexistence in a specific asymmetric kinetic Ising model, combining analytical and numerical methods to understand droplet dynamics and phase boundaries near critical points.

## Contribution

It provides a detailed analysis of phase coexistence and droplet dynamics in a nonequilibrium kinetic Ising model, including exact and numerical results on interface behavior.

## Key findings

- Exact shape of ballistic interfaces at zero temperature via TASEP mapping
- Temperature-dependent droplet shrinking velocity and critical exponents
- Phase boundary fields vanish with specific critical exponents near T_c

## Abstract

The physical analysis of generic phase coexistence in the North-East-Center Toom model was originally given by Bennett and Grinstein. The gist of their argument relies on the dynamics of interfaces and droplets. We revisit the same question for a specific totally asymmetric kinetic Ising model on the square lattice. This nonequilibrium model possesses the remarkable property that its stationary-state measure in the absence of a magnetic field coincides with that of the usual ferromagnetic Ising model. We use both analytical arguments and numerical simulations in order to make progress in the quantitative understanding of the phenomenon of generic phase coexistence. At zero temperature a mapping onto the TASEP allows an exact determination of the time-dependent shape of the ballistic interface sweeping a large square minority droplet of up or down spins. At finite temperature, measuring the mean lifetime of such a droplet allows an accurate measurement of its shrinking velocity $v$, which depends on temperature $T$ and magnetic field $h$. In the absence of a magnetic field, $v$ vanishes with an exponent $\Delta_v\approx2.5\pm0.2$ as the critical temperature $T_c$ is approached. At fixed temperature in the ordered phase, $v$ vanishes at the phase-boundary fields $\pm h_{\rm b}(T)$ which mark the limits of the coexistence region. The latter fields vanish with an exponent $\Delta_h\approx3.2\pm0.3$ as $T_c$ is approached.