A Nonperturbative Study of Inverse Symmetry Breaking at High Temperatures

The optimized linear $\delta$-expansion is applied to multi-field $O(N_1) \times O(N_2)$ scalar theories at high temperatures. Using the imaginary time formalism the thermal masses are evaluated perturbatively up to order $\delta^2$ which considers consistently all two-loop contributions. A variational procedure associated with the method generates nonperturbative results which are used to search for parameters values for inverse symmetry breaking (or symmetry nonrestoration) at high temperatures. Our results are compared with the ones obtained by the one-loop perturbative approximation, the gap equation solutions and the renormalization group approach, showing good agreement with the latter method. Apart from strongly supporting inverse symmetry breaking (or symmetry nonrestoration), our results reveal the possibility of other high temperature symmetry breaking patterns for which the last term in the breaking sequence is $O(N_1-1) \times O(N_2-1)$.