Abstract
Ising models in high dimensions are used to compare high-temperature series expansions with Monte Carlo simulations. Simulations of the magnetization on four-, six-, and seven-dimensional hypercubic lattices give consistent values of the critical temperature from both equilibrium and nonequilibrium data ford=6 and 7. We tabulate 15 terms of series expansions for the susceptibility for generald and giveJ/k B T c =0.092295 (3) and 0.077706 (2) ford=6 and 7. In contrast to five dimensions, where earlier series found nonanalytic scaling corrections, for d=6 and 7 the leading scaling correction may be analytic inT-T c . In most cases these expansions gave more accurate results than these simulations.
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References
M. E. Fisher and D. S. Gaunt,Phys. Rev. 133A:224 (1964).
A. J. Guttmann,J. Phys. A 14:233 (1981).
J. Adler and D. Stauffer,Physica A 181:396 (1992).
C. Münkel, D. W. Heermann, J. Adler, M. Gofman, and D. Stauffer,Physica A 193:540 (1993).
R. J. de Boer, L. A. Segel, and A. S. Perelson,J. Theor. Biol. 155:295 (1992); D. Stauffer and M. Sahimi,Int. J. Mod. Phys. C 4:40 (1993).
K. Binder, ed.,Applications of the Monte Carlo Method in Statistical Physics (Springer-Verlag, Berlin, 1987); D. Stauffer, F. W. Hehl, N. Ito, V. Winkelmann, and J. G. Zabolitzky,Computer Simulation and Computer Algebra, 3rd ed. (Springer-Verlag, Berlin, 1993).
D. Stauffer, Simulation Workshop, Athens, Georgia (February, 1993).
N. Ito,Physica A 192:604 (1993), and preprint; H. O. Heuer,J. Phys. A 25:L567 (1992);26:L333 and L341 (1993).
T. S. Ray,J. Stat. Phys. 62:463 (1991); T. Ala-Nissila, T. Hjelt, J. M. Kosterlitz, and O. Venalainen, preprint (1993).
P. C. Hohenberg and B. I. Halperin,Rev. Mod. Phys. 49:435 (1977), Section IVA; O.G. Mouritsen and S. J. Knak-Jensen,J. Phys. A 12:L339 (1979); B. K. Chakrabarti, H. G. Baumgärtel, and D. Stauffer,Z. Phys. B 44:333 (1981); R. Kenna and C. B. Lang, preprint (1993).
M. Gofman, J. Adler, A. Aharony, A. B. Harris, and M. Schwartz, preprint (1993).
A. B. Harris,Phys. Rev. B 26:337 (1982); A. B. Harris and Y. Meir,Phys. Rev. B 36:1840 (1987).
J. Adler, M. Moshe, and V. Privman,Phys. Rev. B 26:1411 (1982); J. Adler, M. Moshe, and V. Privman,J. Phys. A 14:L363 (1981); J. Adler, M. Moshe, and V. Privman, inAnnals of the Israel Physical Society, Vol. 3, G. Deutscher, R. Zallen, and J. Adler, eds. (Adam Hilger, London, 1983).
J. Adler, Y. Meir, A. Aharony, and A. B. Haris,Phys. Rev. B 41:9183 (1990).
L. Klein, J. Adler, A. Aharony, A. B. Harris, and Y. Meir,Phys. Rev. B 43:11249 (1991).
J. Adler, I. K. Chang, and S. Shapiro, in preparation.
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Gofman, M., Adler, J., Aharony, A. et al. Series and Monte Carlo study of high-dimensional Ising models. J Stat Phys 71, 1221–1230 (1993). https://doi.org/10.1007/BF01049970
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DOI: https://doi.org/10.1007/BF01049970