# Scaling behavior of Ising systems at first-order transitions

## TL;DR

This paper studies how boundary conditions affect the dynamic finite-size scaling behavior of the two-dimensional Ising model at first-order transitions, revealing different scaling regimes and autocorrelation behaviors.

## Contribution

It develops a dynamic finite-size scaling theory for the Ising model at FOTs under various boundary conditions, supported by numerical simulations.

## Key findings

- Boundary conditions influence the scaling behavior at FOTs.
- A power-law autocorrelation time is observed with interface-generating boundary conditions.
- Numerical results confirm the theoretical predictions.

## Abstract

We investigate how the scaling behavior of finite systems at magnetic first-order transitions (FOTs) with relaxational dynamics changes in correspondence of various boundary conditions. As a theoretical laboratory we consider the two-dimensional Ising model in the low-temperature phase. When the boundary conditions do not favor any specific phase of the system, we show that a dynamic finite-size scaling (DFSS) theory can be developed to describe the dynamic behavior in the coexistence region, where different phases coexist. When the boundary conditions at two opposite sides of the system generate a planar interface separating the phases, we show that the autocorrelation times are characterized by a power-law behavior, related to the dynamics enforced by the interface. Numerical results for a purely relaxational dynamics confirm the general picture.