Fluctuation-Driven First-Order Phase Transition, below Four Dimensions, in the Random-Field Ising Model with a Gaussian Random-Field Distribution

Analysis of the high-temperature susceptibility series for the random-field Ising model with a Gaussian distribution of random fields demonstrates the existence of a fluctuation-driven first-order transition below four dimensions, $d<4$. This, and the behavior of the susceptibility exponent in three dimensions, suggest that $d=4$ is a "critical" dimension for the model.