The hysteresis loop in the zero-temperature random-field Ising model e
xhibits 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 t
heory. We expand the critical exponents about mean-field theory, in 6
- epsilon dimensions, to first order in epsilon. Despite epsilon = 3,
the values obtained agree reasonably well with the numerical values in
three dimensions.