The arboreal gas and the supersphere sigma model
Other Condensed Matter
2010-04-05 v1 Statistical Mechanics
High Energy Physics - Theory
Abstract
We discuss the relationship between the phase diagram of the Q=0 state Potts model, the arboreal gas model, and the supersphere sigma model S^{0,2} = OSP(1/2) / OSP(0/2). We identify the Potts antiferromagnetic critical point with the critical point of the arboreal gas (at negative tree fugacity), and with a critical point of the sigma model. We show that the corresponding conformal theory on the square lattice has a non-linearly realized OSP(2/2) = SL(1/2) symmetry, and involves non-compact degrees of freedom, with a continuous spectrum of critical exponents. The role of global topological properties in the sigma model transition is discussed in terms of a generalized arboreal gas model.
Keywords
Cite
@article{arxiv.cond-mat/0502052,
title = {The arboreal gas and the supersphere sigma model},
author = {Jesper Lykke Jacobsen and Hubert Saleur},
journal= {arXiv preprint arXiv:cond-mat/0502052},
year = {2010}
}
Comments
23 pages, 4 figures