Phase transitions leading to structures with nonmaximal symmetry groups

Abstract
A Landau-Ginzburg-Wilson model associated with a single irreducible representation which exhibits an ordered phase whose symmetry group is not a maximal isotropy subgroup of the symmetry group of the disordered phase is constructed. This example disproves the maximality conjecture suggested in numerous previous studies in both phase transitions and Higgs problems. Below the (continuous) transition, the order-parameter points along a direction which varies with the parameters which define the model.