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.

arXiv comment4 pages, 4 figures, 1 table

References in corpus (9)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Critical Coarsening without Surface Tension: the Voter Universality Class
• Universal scaling behavior of non-equilibrium phase transitions
• Directed percolation criticality in turbulent liquid crystals
• Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice
• Epidemic analysis of the second-order transition in the Ziff-Gulari-Barshad surface-reaction model
• The Generation of Turbulence by Oscillating Structures in Superfluid Helium at Very Low Temperatures
• Critical exponents of directed percolation measured in spatiotemporal intermittency
• Reweighting in nonequilibrium simulations

Cited by in corpus (7)

• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Experimental realization of directed percolation criticality in turbulent liquid crystals
• Dynamic scaling at classical phase transitions approached through non-equilibrium quenching
• Experimental approaches to universal out-of-equilibrium scaling laws: turbulent liquid crystal and other developments
• Discontinuous nonequilibrium phase transitions in a nonlinearly pulse-coupled excitable lattice model
• Nonlinear, Nonequilibrium and Collective Dynamics in a Periodically Modulated Cold Atom System
• Phase Transition in a Out-of-equilibrium Monolayer of Dipolar Vibrated Grains