Abstract
The mean field renormalization group method is extended to study tri-critical phenomena. By taking into account the third-order terms in the expansion of the magnetizations of the different clusters with respect to the symmetry breaking fields, together with the scaling assumption of the magnetization at a first-order fixed point, one additional equation is obtained which locates, in an unique manner, the tricritical point. This approach is applied in the study of the classical spin-σ Blume–Capel model and the quantum spin-1/2 anisotropic Heisenberg model in the presence of a transverse field as well as with Dzyaloshinsky–Moriya interactions.
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