Critical Hysteresis

TL;DR

This paper develops universal scaling formulas for hysteresis loop areas at second order phase transitions, relates critical exponents to static and dynamic phenomena, and verifies these relations through simulations in mean-field and two-dimensional Ising models.

Contribution

It introduces universal hysteresis scaling formulas, defines related critical exponents, and validates these relations with numerical simulations across different models.

Findings

Universal hysteresis scaling formulas are verified.

Critical exponents are related to static and dynamic phenomena.

Finite-size scaling is confirmed in the 2D Ising model.

Abstract

Hysteresis is observed at second order phase transitions. Universal scaling formul\ae{} for the areas of hysteresis loops are written down. Critical exponents are defined, and related to other exponents for static and dynamic critical phenomena. These relations are verified with Langevin dynamics in both the critical and tricritical mean-field models. A finite-size scaling relation is tested in the two-dimensional Ising model with heat-bath dynamics. (Shar file; 2 figures created through dvips directives from 4 PS files included)