Absence of symmetry breakdown and uniqueness of the vacuum for multicomponent field theories

Correlation inequalities are used to show that the two component lambda(phi2)2model (with HD, D, HP,P boundary conditions) has a uniquw vacuum if the field does not develop a non-zero expectation vlaue. It follows by a generalized Coleman theorem that in two space-time dimensions the vacuum is unique for all values of the coupling constant. In three space.time dimensions the vacuum is unique below the critical constant. For the n-component P(phi2)2+μphi1 model absence of continuous symmetry breaking, as μ goes to zero, is proven for all states which are translation invariant, satisfy the spectral condition, and are weak limit points of finite volume states satisfying Nsup(t)sub(loc) and higher order estimates. (orig.)