A RIGOROUS BOUND ON THE CRITICAL EXPONENT FOR THE NUMBER OF LATTICE TREES, ANIMALS, AND POLYGONS

Authors
MADRAS N
Citation
N. Madras, A RIGOROUS BOUND ON THE CRITICAL EXPONENT FOR THE NUMBER OF LATTICE TREES, ANIMALS, AND POLYGONS, Journal of statistical physics, 78(3-4), 1995, pp. 681-699
Citations number
15
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Journal of statistical physics → ACNP
ISSN journal
00224715
Volume
78
Issue
3-4
Year of publication
1995
Pages
681 - 699
Database
ISI
SICI code
0022-4715(1995)78:3-4<681:ARBOTC>2.0.ZU;2-8
Abstract
The number of n-site lattice trees (up to translation) is believed to behave asymptotically as Cn(-0)lambda(n), where theta is a critical ex ponent dependent only on the dimension d of the lattice. We present a rigorous proof that theta greater than or equal to (d-1)/d for any d g reater than or equal to 2. The method also applies to lattice animals, site animals, and two-dimensional self-avoiding polygons. We also pro ve that theta greater than or equal to nu when d = 2, where nu is the exponent for the radius of gyration.