Geometric exponents, SLE and logarithmic minimal models

Abstract

In statistical mechanics, observables are usually related to local degrees of freedom such as the Q<4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit, these models are described by rational conformal field theories, namely the minimal models for suitable p,p′. More generally, as in stochastic Loewner evolution (SLEκ), one can consider observables related to non-local degrees of freedom such as paths or boundaries of clusters. This leads to fractal dimensions or geometric exponents related to values of conformal dimensions not found among the finite sets of values allowed by the rational minimal models. Working..