We construct topological defects in two-dimensional classical lattice models and quantum
chains. The defects satisfy local commutation relations guaranteeing that the partition …

In this paper and its sequel, we construct topologically invariant defects in two-dimensional
classical lattice models and quantum spin chains. We show how defect lines commute with …

Percolation models describe the inside of a porous material. The theory emerged timidly in
the middle of the twentieth century before becoming one of the major objects of interest in …

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 …

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 …

A bstract Much of our understanding of critical phenomena is based on the notion of
Renormalization Group (RG), but the actual determination of its fixed points is usually based …

Finding the precise correspondence between lattice operators and the continuum fields that
describe their long-distance properties is a largely open problem for strongly interacting …

We provide a concise exposition with original proofs of combinatorial formulas for the 2D
Ising model partition function, multi-point fermionic observables, spin and energy density …

This book is based on my graduate-course lectures given at the Graduate School of
Mathematics of the University of Tokyo in October 2008 (at the invitation of T. Funaki and M …

We show that the canonical random-cluster measure associated to isoradial graphs is
critical for all q≧1. Additionally, we prove that the phase transition of the model is of the …