Dynamic finite-size scaling at first-order transitions

Abstract

We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. It is characterized by an exponentially large time scale related to the tunneling between the two phases. We show that, when considering time scales of the order of the tunneling time, the dynamic behavior can be described by a two-state coarse-grained dynamics. This allows us to obtain exact predictions for the dynamical scaling functions. To test the general DFSS theory at FOTs, we consider the two-dimensional Ising model in the low-temperature phase, where the external magnetic field drives a FOT, and the 20-state Potts model, which undergoes a thermal FOT. Numerical results for a purely relaxational dynamics fully confirm the general theory.

arXiv comment13 pages

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Cited by in corpus (9)

• 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 dynamics arising from slow round-trip variations of Hamiltonian parameters across quantum and classical critical points
• Dynamical off-equilibrium scaling across magnetic first-order phase transitions
• Scaling behavior of Ising systems at first-order transitions
• 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