Decay of correlations for infinite range interactions in unbounded spin systems

Abstract

In unbounded spin systems at high temperature with two-body potential we prove, using the associated polymer model, that the two-point truncated correlation function decays exponentially (respectively with a power law) if the potential decays exponentially (respectively with a power law). We also give a new proof of the convergence of the Mayer series for the general polymer model. © 1982 Springer-Verlag

Aspects of Ergodic, Qualitative and Statistical Theory of Motion

“…The proliferation of alternative or independent and different proofs, or of nontrivial extensions, shows that in reality the problem is a natural one and that the methods to study it with the techniques of this section are also natural although they are still considered by many as not elegant (and not really natural), and they are avoided when possible or commented by saying that "it must be possible to obtain the same result in a simpler way" (often not followed by any actual work in this direction). An elegant and more general analysis is in [Ca82]. i.e.…”

Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods

“…XIV of this paper) is derived; in (Gallavotti, 1979a) lemma 1 is obtained by literally reducing it to a classical statistical mechanics problem of high temperature expansions for a system of weakly coupled spins, using the techniques of (Kunz, 1978;Sylvester, 1979) later improved in (Cammarota, 1982) [see (Seiler, 1982) for a review].…”

Abstract Polymer Models with General Pair Interactions

“…The authors proved convergence of the pressure via the method of Kirkwood-Salsburg equations. Subsequently, the same system studied in [9] was treated in [18] and [5] via cluster expansion methods based on tree graph inequalities.…”