Extrapolation of lattice gauge theories to the continuum limit
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's are computed for both the free energy and the Wilson function. For the free energy, satisfactory agreement is 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's 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. 14 references.
- Research Organization:
- Columbia Univ., New York (USA). Dept. of Physics
- DOE Contract Number:
- EY-76-C-02-2271
- OSTI ID:
- 6248844
- Report Number(s):
- CU-TP-149; TRN: 79-016503
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
LATTICE FIELD THEORY
GAUGE INVARIANCE
STRONG-COUPLING MODEL
SU-2 GROUPS
U-1 GROUPS
BOUNDARY CONDITIONS
CORRELATION FUNCTIONS
FREE ENERGY
PADE APPROXIMATION
THERMODYNAMICS
THREE-DIMENSIONAL CALCULATIONS
ENERGY
FUNCTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE MODELS
PHYSICAL PROPERTIES
SU GROUPS
SYMMETRY GROUPS
THERMODYNAMIC PROPERTIES
U GROUPS
645400* - High Energy Physics- Field Theory