Abstract Polymer Models with General Pair Interactions

Abstract

polymer models with general pair interactions Aldo ProcacciDep. Matemática-ICEx, UFMG, CP 702 Belo Horizonte -MG, 30161-970 Brazil email: aldo@mat.ufmg.br Abstract A convergence criterion of cluster expansion is presented in the case of an abstract polymer system with general pair interactions (i.e. not necessarily hard core or repulsive). As a concrete example, the low temperature disordered phase of the BEG model with infinite range interactions, decaying polynomially as 1/r d+λ with λ > 0, is studied.

Erratum and Addendum: “Abstract Polymer Models with General Pair Interactions”

“…The rest of the paper [5] is unchanged apart from the following modification in Sect. 4 (BEG model example).…”

“…3 in ref. [5]. In particular, when V (γ i , γ j ) = +∞ we write γ i ∼ γ j and say that γ i and γ j are incompatible; otherwise, when V (γ i , γ j ) ∈ R, we say that γ i and γ j are compatible and write γ i ∼ γ j .…”

“…In [5], taking into account the corrections given in Sects. 1 and 2 of this note, the Kotecký-Preiss criterion has been generalized for polymers interacting through a stable pair potential (in the sense of (1)).…”

“…3.1 of [5] in order to prove there the inequality (3.5) when V (γ i , γ j ) satisfies (1) and F (γ i , γ j ) is defined as in (2). This amounts to prove the following proposition.…”

“…Acknowledgements I am extremely grateful to Alan Sokal for discovering the error in [5]. I also thank David Brydges, Benedetto Scoppola and Simone Severini for useful discussions.…”