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May 2020 Interacting self-avoiding polygons
Volker Betz, Helge Schäfer, Lorenzo Taggi
Ann. Inst. H. Poincaré Probab. Statist. 56(2): 1321-1335 (May 2020). DOI: 10.1214/19-AIHP1003

Abstract

We consider a system of self-avoiding polygons interacting through a potential that penalizes or rewards the number of mutual touchings and we provide an exact computation of the critical curve separating a regime of long polygons from a regime of localized polygons. Moreover, we prove the existence of a sub-region of the phase diagram where the self-avoiding polygons are space filling and we provide a non-trivial characterization of the regime where the polygon length admits uniformly bounded exponential moments.

Dans cet article, nous considérons un système de polygones auto-évitants interagissant au moyen d’un potentiel qui pénalise ou récompense le nombre de points de contacts. Nous calculons la forme exacte de la courbe critique séparant un régime de polygones longs d’un régime de polygones localisés. En outre, nous prouvons l’existence d’un sous-domaine du diagramme de phase dans lequel les polygones remplissent l’espace dans un sens faible et donnons une caractérisation non-triviale du sous-régime où les longueurs des polygones ont des moments exponentiels bornés.

Citation

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Volker Betz. Helge Schäfer. Lorenzo Taggi. "Interacting self-avoiding polygons." Ann. Inst. H. Poincaré Probab. Statist. 56 (2) 1321 - 1335, May 2020. https://doi.org/10.1214/19-AIHP1003

Information

Received: 15 October 2018; Revised: 18 March 2019; Accepted: 7 May 2019; Published: May 2020
First available in Project Euclid: 16 March 2020

zbMATH: 07199899
MathSciNet: MR4076785
Digital Object Identifier: 10.1214/19-AIHP1003

Subjects:
Primary: 60K35, 82B20, 82B27

Rights: Copyright © 2020 Institut Henri Poincaré

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Vol.56 • No. 2 • May 2020
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