Ground state non-universality 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 non-universal. However, we also show that at finite temperature the thermal order parameter exponent one half is restored so that temperature is a relevant variable. The broader implications of these results are discussed.