Abstract

Many statistical models of interacting spins can be reformulated as loop models through high-temperature expansions. At criticality, these models are described by a Conformal Field Theory (CFT). While the spectrum of critical exponents has been known since the late 1980s, the determination of correlation functions in loop models has seen little progress until the recent introduction of conformal bootstrap techniques.

In this talk, I will present our recent derivation of the three-point functions of conformal loop models. Starting from a transfer-matrix approach on the lattice, I will explain how the conformal data emerge in the continuum limit. If time permits, I will also discuss the structure of the space of states of loop models, and show how it leads to the exact computation of general correlation functions.