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Microcanonical scaling in small systems.(English)Zbl 1134.82310

Summary: A microcanonical finite-size scaling ansatz is discussed. It exploits the existence of a well-defined transition point for systems of finite size in the microcanonical ensemble. The best data collapse obtained for small systems yields values for the critical exponents in good agreement with other approaches. The exact location of the infinite system critical point is not needed when extracting critical exponents from the microcanonical finite-size scaling theory.

MSC:

82B27 Critical phenomena in equilibrium statistical mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics

Cite

References:

[1]Barber, M. N., (Domb, C.; Lebowitz, J. L., Phase Transitions and Critical Phenomena, vol. 8 (1983), Academic Press: Academic Press New York), 145
[2]Fisher, M. E.; Barber, M. N., Phys. Rev. Lett., 23, 1516 (1972)
[3]Privman, V.; Fisher, M. E., Phys. Rev. B, 30, 322 (1984)
[4]Gross, D. H.E., Microcanonical Thermodynamics (2001), World Scientific: World Scientific Singapore ·Zbl 0974.82018
[5]Kastner, M.; Promberger, M.; Hüller, A., J. Stat. Phys., 99, 1251 (2000) ·Zbl 1174.82307
[6]Hüller, A.; Pleimling, M., Int. J. Mod. Phys. C, 13, 947 (2002)
[7]Behringer, H., J. Phys. A: Math. Gen., 37, 1443 (2004) ·Zbl 1041.82543
[8]Behringer, H., J. Phys. A: Math. Gen., 36, 8739 (2003) ·Zbl 1161.82314
[9]A. Richter, M. Pleimling, A. Hüller, in preparation; A. Richter, M. Pleimling, A. Hüller, in preparation
[10]de Oliveira, P. M.C.; Penna, T. J.P.; Herrmann, H. J., Braz. J. Phys., 26, 677 (1996)
[11]Promberger, M.; Hüller, A., Z. Phys. B, 97, 341 (1995)
[12]Bhattacharjee, S. M.; Seno, F., J. Phys. A: Math. Gen., 34, 6375 (2001) ·Zbl 0981.82501
[13]Bruce, A. D.; Wilding, N. B., Phys. Rev. E, 60, 3748 (1999)
[14]Kastner, M.; Promberger, M., J. Stat. Phys., 103, 893 (2001) ·Zbl 0989.82019
[15]Hove, J.
[16]Desai, R. C.; Herrmann, D. W.; Binder, K., J. Stat. Phys., 53, 795 (1988)
[17]H. Behringer, On the structure of the entropy surface of microcanonical systems, Ph.D. thesis, Erlangen, 2004; H. Behringer, On the structure of the entropy surface of microcanonical systems, Ph.D. thesis, Erlangen, 2004 ·Zbl 1041.82543
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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