Journal of Statistical Physics, FoL 26, No. 4, 1981 Low-Fugacity Asymptotic Expansion for Classical Lattice Dipole Gases J. R. Fontaine 1 Received April 14, 1981 We consider a classical dipole gas in the grand canonical ensemble. We prove that in dimensions greater than or equal to three, and for all temperatures, the free energy and the charges-dipoles correlation functions have an expansion in powers of z, the fugacity of the system, which is asymptotic to all orders. We also give some information about the decay of correlations. KEY WORDS: Dipole gases; sine-Gordon transformation; charge-charge correlation. 1. INTRODUCTION In this paper we consider a classical lattice system of particles interacting via a dipole potential in the grand canonical ensemble. In this model, particles occupy sites of a lattice Z d, and the (unit) dipole moment of each particle takes one of only a finite number of orientations, namely, the 2d canonical direction of Z d. The potential between two particles located at x and y of dipole moment ex and ey is given by ff J*k [expik(x - y) ](expik. e x - 1)(expik . ey - 1) -1 x 2 (cosk. - l) j=l where ~, j = 1..... d, is the canonical basis of Z d. The thermodynamic limit of the free energy and of the correlation functions of this system in the grand canonical ensemble is known to exist. (5) Since the pair potential is I Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903; on leave from Institut de Physique Th~orique Universit~ de Louvain, Belgium. Supported by N.S.F. grant No. PHY78-15920. 767 0022-4715/81 / 1200-0767503.00/0 9 1981 Plenum Publishing Corporation