We consider the discrete solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schrödinger (NLS) lattice. The discrete soliton in the anti-continuum limit represents an arbitrary finite superposition of in-phase or anti-phase excited nodes, separated by an arbitrary sequence of empty nodes. By using stability analysis, we prove that the discrete solitons are all unstable ...

This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present...

We describe the application of methods from the study of discrete dynamical systems to the study of histories of evolving spin networks. These have been found to describe the small scale structure of quantum general relativity and extensions of them have been conjectured to give background independent formulations of string theory. We explain why the the usual equilibrium second order critical ...

We develop a transfer matrix formalism for two-dimensional pure gravity. By taking the continuum limit, we obtain a “Hamiltonian formalism” in which the geodesic distance plays the role of time. Applying this formalism, we obtain a universal function which describes the fractal structures of two dimensional quantum gravity in the continuum limit. Recent developments of two-dimensional gravity h...

We analyze the Schwinger model on an infinite lattice using the continuum definition of the fermion determinant and a linear interpolation of the lattice gauge fields. The possible class of interpolations for the gauge fields, compatible with gauge invariance is discussed. The effective action for the lattice gauge field is computed for the Wilson formulation as well as for non-compact lattice ...

We show that the initial-state interactions from gluon exchange between the incoming quark and the target spectator system lead to leading-twist single-spin asymmetries in the Drell-Yan process H1H ↑ 2 → `+`−X. The QCD initial-state interactions produce a T−odd spin-correlation ~ SH2 · ~ PH1× ~ Q between the target spin and the virtual photon production plane which is not power-law suppressed i...

We discuss some aspects of the continuum limit of some lattice models, in particular the 2D O(N) models. The continuum limit is taken either in an infinite volume or in a box whose size is a fixed fraction of the infinite volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be O(1) and thus restore the symmetry which may have been broken by t...