Bounds on the zeros of a renormalization group fixed point.
Branching processes, and random-cluster measures on trees
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of ‘boundary condition’, namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of random-cluster measures are explored for certain classes of equivalence relations. In proving uniqueness, the following problem concerning branching processes is encountered and answered. Consider bond percolation on the family-tree of a branching process. What is the...
Central limit theorems for the Potts model.
Classification of subfactors: the reduction to commuting squares.
Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems
The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic lattice systems of interacting particles at equilibrium. The proposed algorithms are derived from an initial coarse-grained approximation that is directly computable by Monte Carlo simulations, and the corresponding numerical error is calculated using the...
Combinatorial analysis of magnetic configurations.
Combinatorics and cluster expansions.
Combinatorics of tripartite boundary connections for trees and dimers.
Complete asymptotics for correlations of Laplace integrals in the semi-classical limit
Continuous and discrete (classical) Heisenberg spin chain revised.
Coordinate Bethe ansatz for spin XXX model.
Decimation on the Two Dimensionnal Ising Model : Non Gibbsianness at Low Temperature. Almost Gibbsianness or Weak Gibbsianness ?
Determinant formulae for some tiling problems and application to fully packed loops
We present a number of determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.
Die Polynome von Yang-Lee und ihre Nullstellen.
Dimers and cluster integrable systems
We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type, which we call acluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space of line bundles with connections on the graph . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs and areequivalentif the Newton polygons of the corresponding partition functions...
Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
Let be a flat surface of genus with cone type singularities. Given a bipartite graph isoradially embedded in , we define discrete analogs of the Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair for these discrete Dirac operators to be Kasteleyn matrices of the graph . As a consequence, if these conditions are met, the partition function of the dimer...
Dynamical critical exponent for two-species totally asymmetric diffusion on a ring.
Dynamics and Lieb-Robinson estimates for lattices of interacting anharmonic oscillators
For a class of infinite lattices of interacting anharmonic oscillators, we study the existence of the dynamics, together with Lieb-Robinson bounds, in a suitable algebra of observables.
Eigenvectors of open Bazhanov-Stroganov quantum chain.
Entanglement transfer through an antiferromagnetic spin chain.