Absence of second-order phase transitions in the Dobrushin uniqueness region

The Dobrushin uniqueness theorem assures that in a very large class of high-temperature classical statistical mechanical lattice models with short or long range, many-body interactions, and arbitrary compact spin space there are no first-order phase transitions. It will be shown that for the same class of interactions there are also no second-order phase transitions.Research partially supported by the National Science Foundation under Grant MCS 78-00688.