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...
Tetrahedron equation and the algebraic geometry
The Bethe lattice spin glass at zero temperature
The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
The -invariance of the Potts Hamiltonian.
The Ising transducer
The phase transition of the number-theoretical spin chain.
The posterior metric and the goodness of gibbsianness for transforms of Gibbs measures.
The representation theory of the Temperley-Lieb algebras.
The shape of a typical boxed plane partition.
The stochastic Ising model with the mixed boundary conditions.
The three dimensional polyominoes of minimal area.
Thermodynamic limit for mean-field spin models.
Three order parameters in quantum spin-oscillator models with Gibbsian ground states.
Two point correlation functions for a periodic box-ball system.
Unique Bernoulli -measures
We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the -measure.