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We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an interface orthogonal to the cylinder axis. Let L be the linear size of the basis of the cylinder. Because of the breaking of the continuous symmetry around the ^ z axis, the(More)
There is still no universally accepted theory of high-temperature superconductivity. Most models assume that doping creates 'holes' in the valence band of an insulating, antiferromagnetic 'parent' compound, and that antiferromagnetism and high-temperature superconductivity are intimately related. If their respective energies are nearly equal, strong(More)
We prove existence of a wetting transition for two types of gradient fields: 1) Continuous SOS models in any dimension and 2) Massless Gaussian model in dimension 2. Combined with a recent result showing the absence of such a transition for Gaussian models above 2 dimensions [5], this shows in particular that absolute-value and quadratic interactions can(More)
The paper concerns lattice triangulations, i.e., triangulations of the integer points in a polygon in R<sup>2</sup> whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects in their own right and by virtue of applications in algebraic geometry. Our focus is on random triangulations in which a(More)
In this work, we adopt a Random Matrix Theory point of view to study the spectrum of large reversible Markov chains in random environment. As the number of states tends to infinity, we consider both the almost sure global behavior of the spectrum , and the local behavior at the edge including the so called spectral gap. We study presently two simple models.(More)