Pseudocritical Phenomena near the Spinodal Point

In a binary mixture, the existence of a spinodal point and the singularity around it are investigated by means of renormalization group method. Since the average concentration c is fixed, the free energy functional contains a cubic term as well as quadratic and quartic terms. A non-trivial fixed point is obtained, which corresponds to the one appearing in the ordinary critical temperature Tc. From linearized recursion relations, a general form of a correlation function is obtained as a function of c and the temperature difference T-Tsp, where Tsp is given by Tc and c. At high temperatures, the correlation function takes a scaling form with non-classical exponents, which proves pseudocritical phenomena. However since a new eigenmode associated with the cubic term is relevant, crossover phenomena happen at a temperature high above Tsp. This means that a true spinodal point does not exist, and the pseudospinodal temperature Tsp can be determined by extrapolation.