Numerical simulations in lattice gauge theories and statistical mechanics

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:5508650

Edwards, R G

A short review of lattice gauge theories is presented along with a review of some standard numerical methods used in lattice computations. The strong-coupling large-N limit of U(N) lattice gauge theory with reduced Dirac-Kaehler lattice fermions is investigated, and the hypercubic symmetry group is used to find the quantum numbers of the mesons and the meson mass spectrum. The latter part of this thesis is concerned with improved algorithms for calculations in lattice gauge theories and statistical mechanics. This discussion falls into two related parts: improved algorithms for the Monte Carlo updating of the gauge fields, and improved algorithms for computing the fermion propagator. A series of statistical-mechanical problems are used as warm-up problems. An improved Monte Carlo method known as Multigrid Monte Carlo (MGMC) is applied to the two-dimensional XY model, and critical-slowing down is found to be eliminated below the transition temperature. Also, MGMC is tested on the O(4)-nonlinear {sigma}-model in two-dimensions. A simple explanation of the Swendsen-Wang (SW) algorithm for q-state Potts models is given in terms of a joint model of Potts spin variables interacting with bond occupation variables. A generalization to continuous fields is developed and applied to the XY model. Results are given of another generalization that augments the SW algorithm in two dimensions with transformations to the dual lattice. the augmented algorithm exhibits an autocorrelation time near zero for temperatures near the bulk transition, for both the first-order (q > 4) and second-order (q {le} 4) transitions. Finally, the problems of solving large linear systems of equations that arise in lattice systems with disorder are discussed.

• Research Organization: New York Univ., NY (United States)
• OSTI ID: 5508650
• Country of Publication: United States
• Language: English

Related Subjects

661300 -- Other Aspects of Physical Science-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
BOSON-EXCHANGE MODELS
BOSONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FIELD THEORIES
HADRONS
HERMITIAN OPERATORS
LATTICE FIELD THEORY
MASS SPECTRA
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
MESONS
MONTE CARLO METHOD
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PERIPHERAL MODELS
PROPAGATOR
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM NUMBERS
SCHROEDINGER EQUATION
SIGMA MODEL
SPECTRA
STATISTICAL MECHANICS
SYMMETRY GROUPS
TRANSFORMATIONS
UNIFIED GAUGE MODELS
WAVE EQUATIONS