Annals of Combinatorics 3 (1999) 277-286

Enumeration of the Self-avoiding Polygons on a Lattice by the Schwinger--Dyson Equations

P. Butera and M. Comi

Istituto Nazionale di Fisica Nucleare, Dipartimento di Fisica, Università di Milano, 16 Via Celoria, 20133 Milano, Italy
{butera, comi}

Received November 1, 1998

AMS Subject Classification: 05A15, 05C38, 82B41

Abstract. We show how to compute the generating function of the self-avoiding polygons on a lattice by using the statistical mechanics Schwinger--Dyson equations for the correlation functions of the N-vector spin model on that lattice.

Keywords: lattice spin models, self-avoiding lattice walks, Schwinger--Dyson equations, static critical phenomena


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