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Block spin renormalization group approach and two-dimensional quantum gravity
Phys. Rev. D 50, 5130 – Published 15 October, 1994
DOI: https://doi.org/10.1103/PhysRevD.50.5130
Abstract
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of two-dimensional quantum gravity. The idea is to update link flips on the block lattice in response to link flips on the original lattice. Just as the connectivity of the original lattice is meant to be a lattice representation of the metric, the block links are determined in such a way that the connectivity of the block lattice represents a block metric. As an illustration, this approach is applied to the Ising model coupled to two-dimensional quantum gravity. The correct critical coupling is reproduced, but the critical exponent is obscured by unusually large finite-size effects.
References (18)
- V. A. Kazakov and A. A. Migdal, Nucl. Phys. B311, 171 (1988).
- R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, New York, 1984).
- D. V. Boulatov and V. A. Kazakov, Phys. Lett. B 186, 379 (1987).
- Z. Burda and J. Jurkiewicz, Acta Phys. Pol. B 20, 9949 (1989).
- V. G. Knizhnik, A. M. Polyakov and A. B. Zamolodchikov, Mod. Phys. Lett. A 3, 819 (1988).
- D. V. Boulatov, V. A. Kazakov, I. K. Kostov and A. A. Migdal, Nucl. Phys. B275, 641 (1986).
- R. L. Renken and J. B. Kogut, Nucl. Phys. B354, 328 (1991).
- S. M. Catterall, J. B. Kogut and R. L. Renken, Phys. Rev. D 45, 2957 (1992).
- For an effort to discuss renormalization group ideas in the context of a random surface theory defined on a regular lattice, see J. Ambjorn et al., J. Stat. Phys. 55, 29 (1989).
- K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975).
- K. G. Wilson, in Recent Developments in Gauge Theories, Proceedings of the Cargese Summer Institute, Cargese, France, 1979, edited by G. 't Hooft et al., NATO Advanced Study Institute Series B: Physics, Vol. 59 (Plenum, New York, 1980).
- R. H. Swendsen, Phys. Rev. Lett. 47, 1775 (1981).
- R. H. Swendsen, J. Appl. Phys. 53, 1920 (1982).
- C. Rebbi and R. H. Swendsen, Phys. Rev. B 21, 4094 (1980).
- M. A. Novotny, D. P. Landau and R. H. Swendsen, Phys. Rev. B 26, 330 (1982).
- M. E. Fisher, Scaling, Universality and Renormalization Group Theory, in Critical Phenomena Lecture Notes in Physics, Vol. 186, edited by F. J. W. Hahne (Springer Verlag, Berlin, 1983).
- Ulli Wolff, Phys. Rev. Lett. 62, 361 (1989).
- G. S. Pawley, R. H. Swendsen, D. J. Wallace and K. G. Wilson, Phys. Rev. B 29, 4030 (1984).