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Title: Renormalization group therapy

Abstract

We point out a general problem with the procedures commonly used to obtain improved actions from Monte Carlo Renormalization Group (MCRG) decimated configurations. Straightforward measurement of the couplings from the decimated configurations, by one of the known methods, can result into actions that do not correctly reproduce the physics on the undecimated lattice. This is because the decimated configurations are generally not representative of the equilibrium configurations of the assumed form of the effective action at the measured couplings. Curing this involves fine-tuning of the chosen MCRG decimation procedure, which is also dependent on the form assumed for the effective action. We illustrate this in decimation studies of the SU(2) lattice gauge theory using Swendsen and 'double smeared blocking' decimation procedures. A single-plaquette improved action involving five group representations and nearly free of this pathology is given.

Authors:
;  [1]
  1. Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547 (United States)
Publication Date:
OSTI Identifier:
21020318
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.75.076002; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; CHANNELING; EQUILIBRIUM; GAUGE INVARIANCE; LATTICE FIELD THEORY; MONTE CARLO METHOD; RENORMALIZATION; SU-2 GROUPS

Citation Formats

Tomboulis, E. T., and Velytsky, A. Renormalization group therapy. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.076002.
Tomboulis, E. T., & Velytsky, A. Renormalization group therapy. United States. doi:10.1103/PHYSREVD.75.076002.
Tomboulis, E. T., and Velytsky, A. Sun . "Renormalization group therapy". United States. doi:10.1103/PHYSREVD.75.076002.
@article{osti_21020318,
title = {Renormalization group therapy},
author = {Tomboulis, E. T. and Velytsky, A.},
abstractNote = {We point out a general problem with the procedures commonly used to obtain improved actions from Monte Carlo Renormalization Group (MCRG) decimated configurations. Straightforward measurement of the couplings from the decimated configurations, by one of the known methods, can result into actions that do not correctly reproduce the physics on the undecimated lattice. This is because the decimated configurations are generally not representative of the equilibrium configurations of the assumed form of the effective action at the measured couplings. Curing this involves fine-tuning of the chosen MCRG decimation procedure, which is also dependent on the form assumed for the effective action. We illustrate this in decimation studies of the SU(2) lattice gauge theory using Swendsen and 'double smeared blocking' decimation procedures. A single-plaquette improved action involving five group representations and nearly free of this pathology is given.},
doi = {10.1103/PHYSREVD.75.076002},
journal = {Physical Review. D, Particles Fields},
number = 7,
volume = 75,
place = {United States},
year = {Sun Apr 01 00:00:00 EDT 2007},
month = {Sun Apr 01 00:00:00 EDT 2007}
}
  • The contractor renormalization group method, a new approach to solving Hamiltonian lattice systems, is presented. The method defines a systematic and nonperturbative means of implementing Kadanoff-Wilson real-space renormalization group transformations using cluster expansion and contraction techniques. We illustrate the approach and demonstrate its effectiveness using scalar field theory, the Heisenberg antiferromagnetic chain, and the anisotropic Ising chain. Future applications to the Hubbard and {ital t}-{ital J} models and lattice gauge theory are discussed. {copyright} {ital 1996 The American Physical Society.}
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