Dorn and Otto (1994) and independently Zamolodchikov and Zamolodchikov (1996)
proposed a remarkable explicit expression, the so-called-M DOZZ formula, for the three …

We show how to combine our earlier results to deduce strong convergence of the interfaces
in the planar critical Ising model and its random-cluster representation to Schramm's SLE …

We rigorously prove the existence and the conformal invariance of scaling limits of the
magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply …

Phase transitions are a central theme of statistical mechanics, and of probability more
generally. Lattice spin models represent a general paradigm for phase transitions in finite …

The conformal bootstrap hypothesis is a powerful idea in theoretical physics which has led
to spectacular predictions in the context of critical phenomena. It postulates an explicit …

This article pertains to the classification of multiple Schramm–Loewner evolutions (SLE). We
construct the pure partition functions of multiple\rm SLE _ κ SLE κ with κ ∈ (0, 4 κ∈(0, 4 and …

In this paper, we consider the set of interfaces between + and - spins arising for the critical
planar Ising model on a domain with + boundary conditions, and show that it converges to …

Conformal loop ensembles (CLEs) are random collections of loops in a simply connected
domain, whose laws are characterized by a natural conformal invariance property. The set of …

These lecture notes provide an (almost) self-contained account on conformal invariance of
the planar critical Ising and FK-Ising models. They present the theory of discrete …

We present exact combinatorial versions of bosonization identities, which equate the
product of two Ising correlators with a free field (bosonic) correlator. The role of the discrete …