Extrapolation of lattice gauge theories to the continuum limit

Journal Article · Wed Aug 15 00:00:00 EDT 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.20.903· OSTI ID:6048276

Duncan, A; Vaidya, H

The problem of extrapolating lattice gauge theories from the strong-coupling phase to the continuum critical point is studied for the Abelian (U(1)) and non-Abelian (SU(2)) theories in three (space-time) dimensions. A method is described for obtaining the asymptotic behavior, for large ..beta.., of such thermodynamic quantities and correlation functions as the free energy and Wilson loop function. Certain general analyticity and positivity properties (in the complex ..beta.. plane) are shown to lead, after appropriate analytic remappings, to a Stieltjes property of these functions. Rigorous theorems then guarantee uniform and monotone convergence of the Pade approximants, with exact pointwise upper and lower bounds. The first three Pade approximants are computed for both the free energy and the Wilson function. For the free energy, we obtain satisfactory agreement with the asymptotic behavior computed by an explicit lattice calculation. The strong-coupling series for the Wilson function is found to be considerably more unstable in the lower-order terms: correspondingly, convergence of the Pade approximants is found to be slower than in the free-energy case. It is suggested that higher-order calculations may allow a reasonably accurate determination of the string constant for the SU(2) theory.

• Research Organization: Department of Physics, Columbia University, New York, New York 10027
• OSTI ID: 6048276
• Journal Information: Phys. Rev., D; (United States), Vol. 20:4
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
LATTICE FIELD THEORY
GAUGE INVARIANCE
STRONG-COUPLING MODEL
CORRELATION FUNCTIONS
COUPLING CONSTANTS
FREE ENERGY
PADE APPROXIMATION
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
SPACE-TIME
SU-2 GROUPS
U-1 GROUPS
ENERGY
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE MODELS
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
SU GROUPS
SYMMETRY GROUPS
THERMODYNAMIC PROPERTIES
U GROUPS
645301* - High Energy Physics- Particle Invariance Principles & Symmetries- General- (-1987)
645400 - High Energy Physics- Field Theory