[phi][sup 4] model near the critical point: The Gaussian variational approximation

Journal Article · Fri Jan 15 04:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.632· OSTI ID:7119787

Kerman, A K; Martin, C ^[1]; Vautherin, D ^[2]

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1. Center for Theoretical Physics, Laboratory for Nuclear Science Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2. Division de Physique Theorique, Institut de Physique Nucleaire, F-91406, Orsay CEDEX (France)

Using the Gaussian variational approximation, we describe the approach to the continuum limit in [phi][sup 4] theory in 3+1 space-time dimensions. We study the solutions of the variational equations and their stability and compare our results with those of Monte Carlo calculations on a lattice. The importance of lattice effects is investigated by putting the Gaussian wave functional on a lattice. We find an abrupt decrease of the fourth derivative of the effective potential in the vicinity of the critical point, which is consistent with Monte Carlo calculations. In the continuum limit [ital b][r arrow]0[sup +], the renormalized theory shows a broken phase which is degenerate with the symmetric phase. In the asymmetric phase the theory is found to be asymptotically free, in agreement with the conclusions of Branchina [ital et] [ital al].

• DOE Contract Number: AC02-76ER03069
• OSTI ID: 7119787
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 47:2; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
CALCULATION METHODS
COUPLING CONSTANTS
EIGENVALUES
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONS
GAUSSIAN PROCESSES
HAMILTONIANS
LATTICE FIELD THEORY
MATHEMATICAL OPERATORS
MONTE CARLO METHOD
PERTURBATION THEORY
PHI4-FIELD THEORY
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RENORMALIZATION
SPACE-TIME
SYMMETRY BREAKING
VARIATIONAL METHODS
WAVE FUNCTIONS