Zeros of partition functions via correlation inequalities

Abstract

We show analyticity of the pressure for some classical ferromagnetic systems in the region ¦Im μ¦ < Re μ of the external field. The proof, via correlation inequalities, is simpler than existing proofs for the Lee and Yang region {Reμ ≠ 0} and applies, without any approximation procedure, to more general continuous spin variables, e.g., distributed as $$\exp ( - \kappa S^{6n} - \lambda S^{4n} + \sum {_{p = 1}^n \sigma _{2p} S^{2p} )} $$ , where σ2n is an arbitrary real number and the other parameters are positive. It also applies directly to plane rotators in the region ¦Im μ¦⩽ ¦Re μ¦ (Euclidean norms), but the proof will be given in a subsequent article, together with new inequalities between truncated correlation functions.