ZEROS OF THE PARTITION-FUNCTION AND GAUSSIAN INEQUALITIES FOR THE PLANE ROTATOR MODEL

The partition function for ferromagnetic plane rotators in a complex external field μ, with |Im μ| ≤ |Re μ |, is bounded below in modulus by its value at μ=0. The proof is based on complex combinations of duplicated variables which are positive definite on a subgroup of the configuration group. In the isotropic situation (and μ=0), the associated Gaussian inequalities" imply that all truncated correlation functions decay at least as the two-point function. © 1979 Plenum Publishing Corporation."