High Temperature Phase Transitions in Two-Scalar Theories with Large $N$ Techniques

Abstract

We consider a theory of a scalar one-component field $\varphi$ coupled to a scalar $N$-component field $\chi$. Using large $N$ techiques we calculate the effective potential in the leading order in $1/N$. We show that this is equivalent to a resummation of an infinite subclass of graphs in perturbation theory, which involve fluctuations of the $\chi$ field only. We study the temperature dependence of the expectation value of the $\varphi$ field and the resulting first and second order phase transitions.

11 pages, LaTex, includes 5 uuencoded postscript figures, OUTP-94-11 P

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