Critical regions at a first-order transition

The author investigates how the Landau theory may break down at a first-order transition (FOT). This may happen because the transition temperature T c is located near two critical points: the metastable critical point (MCP), which is the stability limit of the ordered phase, and the fluid-like critical point (FLCP), at which the conjugate H of the order parameter is not null. Using the Ginzburg criterion, it is found that one inequality expresses the condition that T c be outside the two critical regions. The results are applied to two types of FOT: one located near a tricritical point and the other located near an isolated critical point. When T c is inside a critical region, it is found that the critical indices of the MCP are beta 1 = beta (critical index of the FLCP) and alpha 1 = gamma 1 =1- beta . The critical region (0.2 degrees C) of BaTiO 3 near the FLCP is determined and the experimental results of SbSI and KMnF are discussed.