The global phase diagram of a modular invariant two dimensional statistical model

TL;DR

This paper explores a generalized Coulomb Gas model with modular symmetry, revealing a complex phase diagram with multiple phases, stable fixed points, and connections to conformal field theory and the fractional quantum Hall effect.

Contribution

It introduces a modular invariant Coulomb Gas model, analyzes its phase diagram using renormalization group techniques, and links the findings to conformal field theory and quantum Hall phenomena.

Findings

Infinite phases characterized by dyonic pseudoparticle condensation

Nested global phase diagram with stable fixed points

Connection to 2D conformal field theory and fractional quantum Hall effect

Abstract

A generalization of the Coulomb Gas model with modular SL(2, Z)-symmetry allows for a discrete infinity of phases which are characterized by the condensation of dyonic pseudoparticles and the breaking of parity and time reversal. Here we study the phase diagram of such a model by using renormalization group techniques. Then the symmetry SL(2,Z) acting on the two-dimensional parameter space gives us a nested shape of its global phase diagram and all the infrared stable fixed points. Finally we propose a connection with the 2-dimensional Conformal Field Theory description of the Fractional Quantum Hall Effect.