Rayleigh-Ritz Variational Approximation and Symmetry Nonrestoration

The investigation of symmetry nonrestoration scenarios has led to a controversy, with certain nonperturbative approximation schemes giving indications in sharp disagreement with those found within conventional perturbation theory. A Rayleigh-Ritz variational approach to the problem, which might be useful in bridging the gap between perturbative and nonperturbative viewpoints, is here proposed. As a first application, this approach is used in the investigation of a $Z_2 \times Z_2$-invariant thermal field theory with two scalar fields, placing particular emphasis on the region of parameter space that has been claimed to support symmetry nonrestoration.