The convexity of a scalar effective potential is a well-known property, and, in the situation of spontaneous symmetry breaking, leads to the so-called Maxwell construction, characterized by a flat effective potential between the minima of the bare potential. Simple derivations are given here, which show how linear effective potentials arise from nontrivial saddles points which dominate the partition function, for a self-interacting scalar field and for a Yukawa model.

• Received 17 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.025028