Crossover from first-order and near-spinodal first-order to continuous transitions in the three- and four-state Potts model

A calculation in renormalized perturbation theory, to one-loop order, in $d=6-\epsilon$ dimensions, shows that quadratic-symmetry breaking (QSB) in a continuum-field $p$-state Potts model yields a further distinction between the usual first-order and a "near-spinodal first-order" transition with a metastable state: Whereas the latter can cross over to a continuous transition at a tricritical point with arbitrarily small but finite QSB, the former one requires a QSB above a threshold value. Specific results for the three- and four-state Potts model suggest that this could be used to distinguish experimentally between the two first-order transitions.