Random-field distributions and tricritical points

Abstract

Explicit conditions on the random-field distribution function $p(\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}})$ are given in order to obtain a tricritical point within mean-field theory. At zero field, a minimum [${p}^{(2)}(0)>0$] implies a first-order transition at low temperature. A maximum [${p}^{(2)}(0)<0$] will also induce a first-order transition, provided that ${p}^{(2)}(0){p}^{(6)}(0)<\frac{7}{15}{[{p}^{(4)}(0)]}^{2}$ for ${p}^{(4)}(0)>0$ and ${p}^{(6)}(0)<0$. Otherwise, the transition is second order and there is no tricritical point.