Scaling behaviors at quantum and classical first-order transitions

TL;DR

This paper reviews the finite-size scaling theory for quantum and classical first-order transitions, focusing on equilibrium and out-of-equilibrium dynamics such as quenches and slow protocols.

Contribution

It provides a comprehensive overview of the finite-size scaling behavior at first-order transitions in both quantum and classical systems, including dynamic phenomena.

Findings

Finite-size scaling theory describes large-scale behavior at first-order transitions.

Out-of-equilibrium protocols like quenches are analyzed within this framework.

The review covers both equilibrium and dynamic finite-size effects.

Abstract

We consider quantum and classical first-order transitions, at equilibrium and under out-of-equilibrium conditions, mainly focusing on quench and slow quasi-adiabatic protocols. For these phenomena, we review the finite-size scaling theory appropriate to describe the general features of the large-scale, and long-time for dynamic phenomena, behavior of finite-size systems.