The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non-universal thermodynamic properties beyond meanfield theory. In this contribution we concentrate on these latter aspects of the renormalization group approach. We introduce its main underlying ideas in the familiar context of the ideal Bose gas...

We consider self-adjoint regular Sturm-Liouville problems with positive leading coefficients and weight functions. A new proof of the inequalities among the eigenvalues for separated boundary conditions and those for coupled boundary conditions established recently by three of the authors with M. S. P. Eastham is given. This new proof does not assume that any special case of the inequalities ha...

We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles with compact support propagating over a stationary state depending on only one variable. The direction of propagation is orthogonal to this variable, and the support is concentrated on flat strips of the stationary st...

ü Define the geometry of the system and assign an index number to each cell. Specify the topology by listing the neighbours of each cell. latticevector1 = N@8Sqrt@3D, 0<D;H* for hexagonal lattice *L latticevector2 = N@8Sqrt@3D ê 2, 3 ê 2<D; H* for hexagonal lattice *L addresses = Flatten@Table@8ja, jb<, 8ja, 0, n1 1<, 8jb, 0, n2 1<D, 1D; H* list of lattice addresses of the cells in the patch *L...

New conjectures are proposed on the numbers of FPL configurations pertaining to certain types of link patterns. Making use of the Razumov and Stroganov Ansatz, these conjectures are based on the analysis of the ground state of the Temperley-Lieb chain, for periodic boundary conditions and so-called “identified connectivities”, up to size 2n = 22.

The magnetic ordering due to the long range dipole coupling in an ensemble of magnetic islands is investigated. If the islands are large enough and closely separated, the average dipole energy per island can explain the magnitude of the observed ordering temperature of such an ensemble (U. Bovensiepen et al., J. Magn. Magn. Mater. 192, L386 (1999)). The energetical degeneracy with respect to a ...

We analyse how small irregularities of the solid surface effects the steady flow of a general viscous fluid at larger scales. In particular we consider generalised Stokes system for incompressible non-Newtonian fluids of power-law type with zero Dirichlet boundary conditions when the surface of boundary is rough. Namely, it contains microscopic surface irregularities and an amplitude, and a wav...

J/Ψ and ηc above the QCD critical temperature Tc are studied in anisotropic quenched lattice QCD, considering whether the cc̄ systems above Tc are compact quasi-bound states or scattering states. We adopt the standard Wilson gauge action and O(a)-improved Wilson quark action with renormalized anisotropy as/at = 4 at β = 6.10 on 163 × (14−26) lattices, which correspond to the spatial lattice volu...

Motivated by the analysis of Schrödinger operators with periodic potentials we consider the following abstract situation: Let ∆X be the Laplacian on a non-compact Riemannian covering manifold X with a discrete isometric group Γ acting on it such that the quotient X/Γ is a compact manifold. We prove the existence of a finite number of spectral gaps for the operator ∆X associated with a suitable ...