A remark on high temperature polymer expansion for lattice systems with infinite range pair interactions. (English) Zbl 0929.60088

Procacci, Aldo; de Lima, Bernardo N. B.; Scoppola, Benedetto

Lett. Math. Phys. 45, No. 4, 303-322 (1998).

The formal polymer expansion for high temperature lattice systems is recalled and investigated. The main results concern the expression of the free energy by an absolute convergent expansion series. They are derived, for some absolutely summable infinite range pair potentials, using a “tree equality”, resp. one of two “tree inequalities”. The proofs of the equality, resp. inequalities, are presented in an appendix. The main aim is the exposition based on the tree inequalities instead of other approaches, e.g. on a Rota inequality. (A new proof based on one of the tree inequalities is also given.) Simpler proofs and/or improvements of classical results are obtained.

Reviewer: P.Holicky (Praha)

MSC:

60K40	Other physical applications of random processes
82B20	Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics

Keywords:

polymer expansion; lattice system; tree inequality