The aim of this paper is to deduce a discrete version of the fractional Laplacian in matrix form defined on the 1D periodic (cyclically closed) linear chain of finite length. We obtain explicit expressions for this fractional Laplacian matrix and deduce also its periodic continuum limit kernel. The continuum limit kernel gives an exact expression for the fractional Laplacian (Riesz fractional d...

It has long been argued that the continuum limit of the 3D Ising model is equivalent to a string theory. Unfortunately, in the usual starting point for this equivalence – a certain lattice theory of surfaces – it is not at all obvious how to take the continuum limit. In this note, I reformulate the lattice theory of surfaces in a fashion such that the continuum limit is straightforward. I go on...

We report the results of a Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear σ model. The notable finding is that it agrees very well with both the prediction inspired by Zamolodchikovs’ S-matrix ansatz and with the continuum limit of the dodecahedron spin model. The latter finding renders the existence of asymptotic freedom in the O(3) model rather unlikely. Asymp...

We study discrete vortices in the anti-continuum limit of the discrete two-dimensional non-linear Schrödinger (NLS) equations. The discrete vortices in the anti-continuum limit represent a finite set of excited nodes on a closed discrete contour with a non-zero topological charge. Using the Lyapunov–Schmidt reductions, we find sufficient conditions for continuation and termination of the discre...

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m)-minimal superconformal models coupled to 2D-supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all...

We consider a lattice formulation of the four dimensional N = 1 Wess-Zumino model that uses the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. We show that the corresponding Ward-Takahashi identity is satisfied, both at fixed lattice spacing and in the continuum limit. The calculation is performed in lattice perturbation theory up to order g in the couplin...

A novel method to calculate fB on the lattice is introduced, based on the study of the dependence of finite size effects upon the heavy quark mass of flavoured mesons and on a non–perturbative recursive finite size technique. We avoid the systematic errors related to extrapolations from the static limit or to renormalization aspects of non–relativistic QCD and the results can be extrapolated to...

Upper limits to the one-millimeter continuum flux densities of the high redshift quasars 82 1225 + 31, Ton 490, and PHL 957 are presented. The upper limit to the power observed from these quasars at I mm is, on average, ! the observed power in the continuum at La. These observations are used to constrain the temperature of a hypoth'etical dust shell which reddens the quasar line and continuum e...

1. INTRODUCTION. In the past thirty or forty years inverse limits have been used extensively in dynamical systems as well as in continuum theory as a means to attack a myriad of unsolved problems. A study of one-dimensional branched manifolds by R. F. Williams [16] provided an early demonstration of the utility of the inverse limit construction in dynamical systems. In continuum theory, many su...