Related papers: Size and area of square lattice polygons
Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the…
A new algorithm for the derivation of low-density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems. Numerical evidence shows that the computational complexity grows…
We report site percolation thresholds for square lattice with neighbor interactions at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (N$^2$), next nearest neighbors (N$^3$), next next nearest…
In a previous article it was shown that when a three-dimensional smooth convex body has rotational symmetry around a coordinate axis one can find better bounds for the lattice point discrepancy than what is known for more general convex…
I begin by discussing the basic ideas of quantum field theory (QFT). I provide a review of symmetries in physics and then move on to discuss the quark model. I then review lattice gauge theory with particular attention paid to lattice QCD…
A small polygon is a polygon of unit diameter. The maximal area of a small polygon with $n=2m$ vertices is not known when $m\ge 7$. Finding the largest small $n$-gon for a given number $n\ge 3$ can be formulated as a nonconvex quadratically…
Because the time needed for a simulation in lattice QCD varies at a rate exceeding the fourth power of the lattice size, it is important to understand how small one can make a lattice without altering the physics beyond recognition. It is…
We study the connection between the theory of spherical designs and the question of extrema of the height function of lattices. More precisely, we show that a full-rank n-dimensional Euclidean lattice, all layers of which hold a spherical…
We calculate the area of the smallest triangle and the area of the smallest virtual triangle for many known lattice surfaces. We show that our list of the lattice surfaces for which the area of the smallest virtual triangle greater than .05…
We perform a lattice QCD calculation of the $\eta_c\to2\gamma$ decay width using a model-independent method that requires no momentum extrapolation of the off-shell form factors. This method also provides a straightforward and simple way to…
We develop a recursive formula for counting the number of rectangulations of a square, i.e the number of combinatorially distinct tilings of a square by rectangles. Our formula specializes to give a formula counting generic rectangulations,…
We present a general class of unbiased improved estimators for physical observables in lattice gauge theory computations which significantly reduces statistical errors at modest computational cost. The error reduction techniques, referred…
A review of the theoretical approach for calculating the resistance between two arbitrary lattice points in an infinite square lattice (perfect and perturbed cases)is carried out using the Lattice Green's Function. We show how to calculate…
We report on the exact treatment of a random-matrix representation of bond percolation model on a square lattice in two dimensions with occupation probability $p$. The percolation problem is mapped onto a random complex matrix composed of…
The low-temperature series are calculated for the free energy, magnetization and susceptibility in the Q-state Potts model on the square lattice, using the improved algorithm of the finite lattice method. The series are obtained to the…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
We state the formula for the critical number of vertices of a convex lattice polygon that guarantees that the polygon contains at least one point of a given sublattice and give a partial proof of the formula. We show that the proof can be…
Progress on the calculation of the spectrum from lattice calculations is reviewed. Particular emphasis is placed on discussing our ability to control possible systematic errors coming from finite volume, and extrapolations in quark mass and…
We present some aspects of high precision calculations in the context of Lattice Quantum Field Theory. This work is a collection of three studies done during my Ph.D. period. First we present how to use the reweighting technique to…
The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can…