Series and Monte Carlo study of high-dimensional Ising models |
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| Authors: | Misha Gofman Joan Adler Amnon Aharony A. B. Harris Dietrich Stauffer |
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| Affiliation: | (1) School of Physics and Astronomy, Beverly and Raymond Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel Aviv, Israel;(2) Department of Physics, Technion-IIT, 32000 Haifa, Israel;(3) Department of Physics, University of Pennsylvania, 19104 Philadelphia, Pennsylvania;(4) Institute of Theoretical Physics, Cologne University, D-50923 Cologne 41, Germany |
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| 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/kBTc=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-Tc. In most cases these expansions gave more accurate results than these simulations. |
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| Keywords: | Series expansions Monte Carlo simulation Ising models corrections to scaling |
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