Tricritical scaling in the spherical model limit

Abstract

The tricritical scaling properties of the n‐component continuous‐spin model are investigated in the sphercal model limit, n→∞, with special emphasis on the odd fields h and h₃. A full scaling description of the tricritical region for 3<dp, related to the inverse range of the pair interaction. As the lambda line in zero field (h=h₃=0) is approached, p becomes important and determines the correct spherical model exponents. Setting p=0 gives only classical theory; away from the lambda line p yields corrections to scaling of Gaussian character. The wing critical exponents arising for h≠0, h₃=0 and T<T_t are classical. Furthermore, for h₃≠0 classical behavior is found even on the lambda line above T_t which, in fact, continues into one of the wing critical lines. Some consequences for real tricritical behavior are reviewed.