Tricritical points in systems with random fields

Mean-field theory and renormalization-group arguments are used to show that the phase transition in a system with a random ordering field becomes first order at sufficiently low transition temperature, provided the (symmetric) random-field distribution function has a minimum at zero field. The first-order region is separated from the second-order region by a tricritical point. Both the critical and the tricritical exponents at $d>\mathrm{}4\mathrm{}$ dimensions are shown to be the same as for the pure system at $d-2\mathrm{}$ dimensions. The relevance to spin glasses and other systems is discussed. The new tricritical point is very different from all previously studied tricritical points, as it deviates from mean-field theory at $d=5\mathrm{}$, and not at $d=3\mathrm{}$. Although quantitative results are calculated only at $d=5-\epsilon$ dimensions, the qualitative results are expected to apply at $d=3\mathrm{}$.