Dualities between fermionic theories and the Potts model

Abstract

We show that a large class of fermionic theories are dual to a $q\to 0$ limit of the Potts model in the presence of a magnetic field. These can be described using a statistical model of random forests on a graph, generalizing the (unrooted) random forest description of the Potts model with only nearest neighbor interactions. We then apply this to find a statistical description of a recently introduced family of $OSp(1|2M)$ invariant field theories that provide a UV completion to sigma models with the same symmetry.

19 pages, 6 figures

References in corpus (7)

• Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
• Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
• Grassmann Integral Representation for Spanning Hyperforests
• Functional RG approach to the Potts model
• Critical Field Theories with OSp$(1|2M)$ Symmetry
• Spanning Forests on Random Planar Lattices
• A Flow in the Forest