Violation of finite-size scaling in three dimensions |
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Authors: | XS Chen V Dohm |
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Institution: | (1) Institut für Theoretische Physik, Technische Hochschule Aachen, 52056 Aachen, Germany, DE;(2) Institute of Particle Physics, Hua-Zhong Normal University, Wuhan 430079, PR China, CN |
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Abstract: | We reexamine the range of validity of finite-size scaling in the lattice model and the field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of
the theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite
cutoff. For a confined geometry of linear size L with periodic boundary conditions we analyze the approach towards bulk critical behavior as at fixed for where is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On
the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for
both the lattice model and the field theory in the region . The non-scaling effects in the field theory and in the lattice model differ significantly from each other.
Received 5 February 1999 |
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Keywords: | PACS 05 70 Jk Critical point phenomena - 64 60 -i General studies of phase transitions |
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