Renormalization Group Analysis of Finite-Size Scaling in the $Φ^4_4$ Model

Details Renormalization Group Analysis of Finite-Size Scaling in the $Φ^4_4$ Model Renormalization Group Analysis of Finite-Size Scaling in the $Φ^4_4$ Model

1992-10-07

arxiv.org/abs/hep-lat/9210009v2

Nucl.Phys. B393 (1993) 461-479; Erratum-ibid. B411 (1994) 340

Physics

High Energy Physics

High Energy Physics - Lattice

25 p + 3 PS-figures, UNIGRAZ-UTP-07-10-92 (Revision 08-10-92: only PS-figures, which originally had too long lines exceeding 8

Scientific paper

10.1016/0550-3213(93)90068-Z

A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the leading scaling behaviour is identical to that of mean field theory, there exist multiplicative logarithmic corrections too. A non-perturbative test of these formulae in the form of a high precision Monte Carlo analysis reveals good quantitative agreement with the analytical predictions.

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