Monte Carlo and renormalization-group effective potentials in scalar field theories

Journal Article · Thu Jun 15 04:00:00 EDT 1995 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.51.7017· OSTI ID:55220

Shepard, J R; Dmitrasinovic, V ^[1]; McNeil, J A ^[2]

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1. Department of Physics, University of Colorado, Boulder, Colorado 80309-0446 (United States)
2. Department of Physics, Colorado School of Mines, Golden, Colorado 80401 (United States)

We study constraint effective potentials for various strongly interacting {phi}{sup 4} theories. Renormalization-group (RG) equations for these quantities are discussed and a heuristic development of a commonly used RG approximation is presented which stresses the relationships among the loop expansion, the Schwinger-Dyson method, and the renormalization-group approach. We extend the standard RG treatment to account explicitly for finite lattice effects. Constraint effective potentials are then evaluated using Monte Carlo (MC) techniques and careful comparisons are made with RG calculations. An explicit treatment of finite lattice effects is found to be essential in achieving quantitive agreement with the MC effective potentials. Excellent agreement is demonstrated for {ital d}=3 and {ital d}=4, O(1) and O(2) cases in both symmetric and broken phases.

• OSTI ID: 55220
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 12 Vol. 51; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
CONSTRAINTS
EXPANSION
FOUR-DIMENSIONAL CALCULATIONS
MONTE CARLO METHOD
O GROUPS
PHI4-FIELD THEORY
POTENTIALS
SCALAR FIELDS
SCHWINGER FUNCTIONAL EQUATIONS
THREE-DIMENSIONAL CALCULATIONS