Extrema of Landau and Higgs Polynomials and Fixed Points of Renormalization-Group Equations

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Abstract
A powerful method is presented for solving systems of nonlinear equations such as those occurring in the Landau theory of phase transitions, in the Higgs mechanism of spontaneous symmetry breaking, and in renormalization-group studies of critical phenomena. As an illustration a ferroelectric phase transition in perovskites is considered with the most general free energy of sixth degree. A special case is a fourth-degree potential which corresponds, e.g., to an SO(7), adjoint representation, Higgs problem.