Monte Carlo Renormalization Group Study of $\phi^4$ Field Theory

Callaway, David J.E.; Petronzio, Roberto

doi:10.1016/0550-3213(84)90246-3

Monte Carlo Renormalization Group Study of $\phi^4$ Field Theory

David J.E. Callaway
(
- CERN
)
,
Roberto Petronzio
(
- CERN
)

Mar, 1984

11 pages

Published in:

Nucl.Phys.B 240 (1984) 577-587

Published: 1984

DOI:

10.1016/0550-3213(84)90246-3

Report number:

CERN-TH-3844

View in:

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Abstract: (Elsevier)

A previously proposed general method for evaluating block renormalized coupling constants within the framework of the Monte Carlo renormalization group (MCRG) is applied to φ 4 field theory. The flow diagrams, fixed points, and critical exponents are determined in two, three and four dimensions. Results in four dimensions are consistent with the idea that φ 4 field theory is trivial (non-interacting) in the continuum limit. The possibility of using MCRG techniques to ascertain whether a general non-asymptotically free theory is trivial or not is also discussed.

field theory: scalar
LATTICE FIELD THEORY: TWO-DIMENSIONAL
LATTICE FIELD THEORY: THREE-DIMENSIONAL
LATTICE FIELD THEORY: FOUR-DIMENSIONAL
LATTICE FIELD THEORY: CRITICAL PHENOMENA
STATISTICAL MECHANICS: ISING
RENORMALIZATION GROUP
COUPLING CONSTANT
NUMERICAL CALCULATIONS: MONTE CARLO

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