Sampling 3-colourings of regular bipartite graphs.
Scaling limit of isoradial dimer models and the case of triangular quadri-tilings
Solvable lattice model and representation theory of quantum affine algebras.
Some non-markovian Osterwalder-Schrader fields
Spectral gap and logarithmic Sobolev inequality for unbounded conservative spin systems
Spin chain connected to the quantum superalgebra .
Spin chains with non-diagonal boundaries and trigonometric SOS model with reflecting end.
Spontaneous breaking of continuous rotational symmetry in two dimensions.
Stochastic domination : the contact process, Ising models and FKG measures
Surface energies in a two-dimensional mass-spring model for crystals
We study an atomistic pair potential-energy E(n)(y) that describes the elastic behavior of two-dimensional crystals with natoms where characterizes the particle positions. The main focus is the asymptotic analysis of the ground state energy asn tends to infinity. We show in a suitable scaling regime where the energy is essentially quadratic that the energy minimum of E(n) admits an asymptotic expansion involving fractional powers of n: The bulk energy densityEbulk is given by an explicit expression...
Surface energies in a two-dimensional mass-spring model for crystals
We study an atomistic pair potential-energy E(n)(y) that describes the elastic behavior of two-dimensional crystals with n atoms where characterizes the particle positions. The main focus is the asymptotic analysis of the ground state energy as n tends to infinity. We show in a suitable scaling regime where the energy is essentially quadratic that the energy minimum of E(n) admits an asymptotic expansion involving fractional powers of n: The bulk energy density Ebulk is given by an explicit expression...
Symmetries of an extended Hubbard Model
The Hamiltonian for an extended Hubbard model with phonons as introduced by A. Montorsi and M. Rasetti is considered on a D-dimensional lattice. The symmetries of the model are studied in various cases. It is shown that for a certain choice of the parameters a superconducting holds as a true quantum symmetry, but only for D=1.
Systems with Coulomb interactions
Systems with Coulomb and logarithmic interactions arise in various settings: an instance is the classical Coulomb gas which in some cases happens to be a random matrix ensemble, another is vortices in the Ginzburg-Landau model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. In this review, we describe...