Self-Organized Criticality with Continuously Varying Exponents

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 H 0 and ω, the area of the hysteresis loop scales as ( H 0 ω) α , where H 0 is the amplitude and ω the frequency of the external field, and α is an exponent which varies continuously from 1/2 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.