Continuous symmetry breaking in closed intervals of the temperature axis and the Ising-, XY- and Heisenberg models

Performing a new transformation on the partition function of the Ising-, anisotropic XY- and Heisenberg models, the existence of continuous symmetry breaking is proved on intervals of the temperature axis below the exact, maximal critical temperature Tsub(cm). In the anisotropic case the exact, maximal critical temperature does depend on the anisotropic parameter of the coupling constant. The continuous symmetry breaking occurs in the presence of homogeneous or inhomogeneous, external, magnetic fields. It is shown for the XY-model with inhomogeneous, external field in the z-direction that this model also possesses continuous symmetry breaking on intervals of the temperature axis below the exact, maximal critical temperature. The relation of this model to the BCS-model is apparent, therefore the isothermal, local resistivity is discussed for the model. It is proved that the isothermal, local resistivity is zero in the associated superconducting state. (Auth.)