Scaling of hysteresis loops at phase transitions into a quasiabsorbing state

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 $\kappa =1/({\beta }^{\prime }+1)$, where ${\beta }^{\prime }$ 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.

4 pages, 4 figures, 1 table

References in corpus (1)

• Directed percolation criticality in turbulent liquid crystals

Cited by in corpus (2)

• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Nonlinear, Nonequilibrium and Collective Dynamics in a Periodically Modulated Cold Atom System