ar X iv : m at h - ph / 9 90 80 30 v 2 2 1 O ct 1 99 9 Nonlinear Hodge maps

ar X iv : m at h - ph / 9 90 80 30 v 1 3 1 A ug 1 99 9 Nonlinear Hodge maps

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Continuity results are given for the tra...

ar X iv : m at h - ph / 9 91 00 13 v 1 8 O ct 1 99 9 q - deformed

ar X iv : h ep - l at / 9 90 90 59 v 2 2 O ct 1 99 9

We investigate a number of algorithms that calculate the quark propagators for the overlap-Dirac fermion operator. The QCD simulations were performed at β = 5.9 with a lattice volume of 16 3 32.

ar X iv : m at h - ph / 9 90 40 25 v 1 2 6 A pr 1 99 9 TRACE MAPS , INVARIANTS , AND SOME OF THEIR APPLICATIONS

Trace maps of two-letter substitution rules are investigated with special emphasis on the underlying algebraic structure and on the existence of invariants. We illustrate the results with the generalized Fibonacci chains and show that the well-known Fricke character I(x, y, z) = x 2 + y 2 + z 2 − 2xyz − 1 is not the only type of invariant that can occur. We discuss several physical applications...

ar X iv : 0 80 9 . 42 29 v 2 [ m at h - ph ] 1 4 O ct 2 00 8 Thermodynamic Limit for Spin Glasses . Beyond the Annealed Bound

Using a correlation inequality of Contucci and Lebowitz for spin glasses, we demonstrate existence of the thermodynamic limit for short-ranged spin glasses, under weaker hypotheses than previously available, namely without the assumption of the annealed bound.