The large-N limit and the high-temperature phase transition for the φ4 theory

We study, with various methods (standard large N evaluation of the functional integral for the effective potential, solution of the Schwinger-Dyson equations), the high temperature phase transition for the Ncomponent \phi^4theory in the large Nlimit. Our results fully confirm a previous investigation of the problem, for arbitrary N with the method of the average potential which employs renormalization group ideas. The phase...