The arboreal gas and the supersphere sigma model

Jesper Lykke Jacobsen; Hubert Saleur

doi:10.1016/j.nuclphysb.2005.04.001

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The arboreal gas and the supersphere sigma model

Jesper Lykke Jacobsen·Hubert Saleur

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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.

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Jesper Lykke Jacobsen, Hubert Saleur. 2005-02-02. The arboreal gas and the supersphere sigma model. https://doi.org/10.1016/j.nuclphysb.2005.04.001

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