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Measures of critical exponents in the four-dimensional site percolation

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1997-05-15
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Elsevier Science BV
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Using finite-size scaling methods we measure the thermal and magnetic exponents of the site percolation in four dimensions, obtaining a value for the anomalous dimension very different from the results found in the literature. We also obtain the leading corrections-to-scaling exponent and, with great accuracy, the critical density.
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@ 1997 Published by Elsevier Science B.V. We thank the CICyT (contracts AEN94-0218, AEN96-1634) for partial financial support, specially for the financing of dedicated Pentium Pro machines where most of the simulations have been done. J.J.R.L. is supported by an EC HMC (ERBFMBICT950429) grant.
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1) D. Stauffer, A. Aharony, An Introduction to the Percolation Theory (Taylor & Francis, London, 1994). 2) P.W. Kasteleyn, C.M. Fortuin, J. Phys. Sot. Japan, 26 (Suppl) (1969) 11. 3) O.F. de Alcántara, J.E. Kirkham, A.J. McKane, J. Phys. A, 13 (1980) L247 -- ibid., 14 (1981) 2391 and references therein. 4) B. Nienhuis, J. Phys. A, 15 (1982) 199. 5) G. Parisi, E. Fucito, J. Phys. A, 14 (1981) L507. 6) H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, Phys. Lett. B, 378 ( 1996) 207 -- ibid., B, 387 ( 1996) 125 -- ibid., Nucl. Phys. B, 483 (1997). 7) G. Parisi, J.J. Ruiz-Lorenzo, J. Phys. A, 28 (1995) L395. 8) D.J. Amit, Field Theory, the Renormalization Group and Critical Phenomena, 2nd Ed. (World Scientific, Singapore, 1984). 9) G. Parisi, Field Theory, Disorder and Simulations (World Scientific, Singapore, 1994). 10) H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, J.J. Ruiz-Lorenzo, work in progress. 11) G. Parisi, F. Rapuano, Phys. Lett. B, 157 (1985) 301. 12) G. Harris, Nucl. Phys. B, 418 (1994) 278. 13) F. Cooper, B. Freedman, D. Preston, Nucl. Phys. B, 210 (1989) 210. 14) K. Binder, Z. Phys. B, 43 (1981) 119. 15) J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon Press, Oxford, 1993).
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