Existence of phase transitions near the displacive limit of a classical n-component lattice model

Using a new method proposed by Fröhlich, Simon, and Spencer, we prove the existence of a phase transition near the displacive limit of a classical n-component displacement model on a d-dimensional (d3) lattice. In certain cases, the proof can be extended for d=2 and n=1. Moreover, we derive exact lower bounds for the critical temperature of the spin-s (s=12, 1, 32,...) extension of the Blume-Capel model. © 1977 The American Physical Society.