Scaling of hysteresis loops at phase transitions into a quasiabsorbing state

TL;DR

This paper investigates how hysteresis loop widths scale with ramp rate in models transitioning to an absorbing state, revealing algebraic relationships explained by critical exponents and supported by simulations and experiments.

Contribution

It introduces a theoretical framework linking hysteresis scaling to critical exponents in phase transitions into a quasi-absorbing state, supported by analytical and numerical evidence.

Findings

Hysteresis width scales as a power law with ramp rate.

Analytical derivation of the scaling exponent.

Experimental relevance demonstrated through liquid crystal convection.

Abstract

Models undergoing a phase transition to an absorbing state weakly broken by the addition of a very low spontaneous nucleation rate are shown to exhibit hysteresis loops whose width $\Delta\lambda$ depends algebraically on the ramp rate $r$. Analytical arguments and numerical simulations show that $\Delta\lambda \sim r^{\kappa}$ with $\kappa = 1/(\beta'+1)$, where $\beta'$ is the critical exponent governing the survival probability of a seed near threshold. These results explain similar hysteresis scaling observed before in liquid crystal convection experiments. This phenomenon is conjectured to occur in a variety of other experimental systems.