Ground state nonuniversality in the random-field Ising model

Two attractive and often used ideas, namely, universality and the concept of a zero-temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are nonuniversal. However, we also show that at finite temperature the thermal order-parameter exponent $1/2$ is restored so that temperature is a relevant variable. Broader implications of these results are discussed.