Classical dimers with aligning interactions on the square lattice

Fabien Alet, Yacine Ikhlef, Jesper Lykke Jacobsen, Grégoire Misguich, and Vincent Pasquier
Phys. Rev. E 74, 041124 – Published 26 October 2006

Abstract

We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and transfer matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the noninteracting case of dimer coverings, including a Bethe ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model, and a free field analysis of height fluctuations.

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  • Received 28 July 2006

DOI:https://doi.org/10.1103/PhysRevE.74.041124

©2006 American Physical Society

Authors & Affiliations

Fabien Alet1,2,*, Yacine Ikhlef3,2, Jesper Lykke Jacobsen3,2, Grégoire Misguich2, and Vincent Pasquier2

  • 1Laboratoire de Physique Théorique, UMR CNRS 5152, Université Paul Sabatier, 31062 Toulouse, France
  • 2Service de Physique Théorique, URA CNRS 2306, CEA Saclay, 91191 Gif sur Yvette, France
  • 3LPTMS, UMR CNRS 8626, Université Paris-Sud, 91405 Orsay, France

  • *Electronic address: alet@irsamc.ups-tlse.fr

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Issue

Vol. 74, Iss. 4 — October 2006

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