Hysteresis loop critical exponents in 6-ε dimensions

The hysteresis loop in the zero-temperature random-field Ising model exhibits a critical point as the width of the disorder increases. Above six dimensions, the critical exponents of this transition, where the ‘‘infinite avalanche’’ first disappears, are described by mean-field theory. We expand the critical exponents about mean-field theory, in 6-ε dimensions, to first order in ε. Despite ε=3, the values obtained agree reasonably well with the numerical values in three dimensions.