The arboreal gas and the supersphere sigma model

Details The arboreal gas and the supersphere sigma model The arboreal gas and the supersphere sigma model

2005-02-02

arxiv.org/abs/cond-mat/0502052v1

Nucl.Phys. B716 (2005) 439-461

Physics

Condensed Matter

Other Condensed Matter

23 pages, 4 figures

Scientific paper

10.1016/j.nuclphysb.2005.04.001

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.

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