Self-organized criticality with continuously varying exponents

Abstract

We consider the hysteretic response of a system of two-dimensional planar spins in contact with a heat bath, to a uniform external magnetic field varying sinusoidally in time. The temperature is below the Kosterlitz-Thouless transition temperature T_KT. We show that for small H₀ and ω, the area of the hysteresis loop scales as (H₀ω)^α, where H₀ is the amplitude and ω the frequency of the external field, and α is an exponent which varies continuously from ½ to 16/31, as the temperature increases from zero to T_KT. This is an example of a driven dissipative system which shows self-organized criticality with continuously varying exponents.