Scaling behavior of Ising systems at first-order transitions

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.

arXiv comment18 pages, 8 figures

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Cited by in corpus (6)

• Coherent and dissipative dynamics at quantum phase transitions
• Scaling properties of the dynamics at first-order quantum transitions when boundary conditions favor one of the two phases
• Out-of-equilibrium scaling behavior arising during round-trip protocols across a quantum first-order transition
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models
• Spinodal-like scaling behavior after a temperature quench across the first-order phase transition in three-dimensional $q$-state Potts models