Abstract
In this lecture we first discuss “static” single- and multiple-histogram reweighting methods and then move on to “dynamic” updating methodologies related to histogramming. Specifically we will consider the multicanonical approach and tempering methods. The methods are illustrated with applications to systems exhibiting first-order phase transitions and spin glasses.
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References
A. M. Ferrenberg and R.H. Swendsen, Phys. Rev. Lett. 61 (1988) 2635; ibid. 63 (1989) 1658 (Erratum).
B. Kaufman, Phys. Rev. 76 (1949) 1232.
A. E. Ferdinand and M. E. Fisher, Phys. Rev. 185 (1969) 832.
P. D. Beale, Phys. Rev. Lett. 76 (1996) 78.
N. B. Wilding, Computer Simulation of Continuous Phase Transitions, this volume.
W. Janke, First-Order Phase Transitions, this volume.
A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 63 (1989) 1195.
W. Janke, Statistical Analysis of Simulations: Data Correlations and Error Estimation, in: Proceedings of the Euro Winter School Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, edited by J. Grotendorst, D. Marx, and A. Muramatsu, John von Neumann Institute for Computing, Jülich, NIC Series, Vol. 10 (2002), pp. 423–445 [http://www.fz-juelich.de].
C. Holm and W. Janke, Phys. Rev. B 48 (1993) 936.
B. A. Berg, Introduction to Multicanonical Monte Carlo Simulations, Fields Inst. Comm. 26 (2000) 1 [cond-mat/9909236]; Generalized Ensemble Simulations for Complex Systems, Comp. Phys. Comm. 104 (2002) 52.
W. Janke, Multicanonical Monte Carlo Simulations, Physica A 254 (1998) 164.
B. A. Berg and T. Neuhaus, Phys. Lett. B 267 (1991) 249.
B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68 (1992) 9.
K. Binder, in: Phase Transitions and Critical Phenomena, Vol. 5b, eds. C. Domb and M. S. Green (Academic Press, New York, 1976), p. 1.
W. Janke, Int. J. Mod. Phys. C 3 (1992) 1137.
G. M. Torrie and J. P. Valleau, Chem. Phys. Lett. 28 (1974) 578; J. Comp. Phys. 23 (1977) 187; J. Chem. Phys. 66 (1977) 1402; I. S. Graham and J. P. Valleau, J. Phys. Chem. 94 (1990) 7894; J. P. Valleau, J. Comp. Phys. 96 (1991) 193.
D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, Oxford, 1987), pp. 168–175.
W. Janke and T. Sauer, Phys. Rev. E 49 (1994) 3475.
W. Janke and T. Sauer, J. Stat. Phys. 78 (1995) 759.
W. Janke and S. Kappler, Phys. Rev. Lett. 74 (1995) 212; M. S. Carroll, W. Janke, and S. Kappler, J. Stat. Phys. 90 (1998) 1277.
B. A. Berg, U. Hansmann, and T. Neuhaus, Phys. Rev. B 47 (1993) 497.
B. A. Berg, U. Hansmann, and T. Neuhaus, Z. Phys. B 90 (1993) 229.
B. Hesselbo and R. Stinchcombe, Phys. Rev. Lett. 74 (1995) 2151.
B. A. Berg and T. Celik, Phys. Rev. Lett. 69 (1992) 2292.
J. Lee, Phys. Rev. Lett. 71 (1993) 211; ibid. 71 (1993) 2353 (Erratum).
B. A. Berg, U. Hansmann, and Y. Okamoto, J. Phys. Chem. 99 (1995) 2236.
B. A. Berg, J. Stat. Phys. 82 (1996) 323.
G. R. Smith and A. D. Bruce, J. Phys. A28 (1995) 6623; Phys. Rev. E 53 (1996) 6530.
M. J. Thill, preprints cond-mat/9703234 and cond-mat/9703233.
B. A. Berg and W. Janke, unpublished notes.
F. Wang and D. P. Landau, Phys. Rev. Lett. 86 (2001) 2050; Phys. Rev. E 64 (2001) 056101.
D. P. Landau, Accelerated Algorithms I: Lattice Models, this volume.
U. H. Hansmann and Y. Okamoto, J. Comp. Chem. 14 (1993) 1333; M.-H. Hao and H. A. Scheraga, J. Phys. Chem. 98 (1994) 4940; U. H. Hansmann and Y. Okamoto, Ann. Rev. Comp. Phys. 6 (1999) 129; A. Mitsutake, Y. Sugita, and Y. Okamoto, Biopolymers (Peptide Science) 60 (2001) 96.
T. Neuhaus and J. S. Hager, preprint cond-mat/0201324.
K. Leung and R. K. P. Zia, J. Phys. A 23 (1990) 4593.
C. Borgs and S. Kappler, Phys. Lett. A 171 (1992) 37.
A. Billoire, T. Neuhaus, and B. Berg, Nucl. Phys. B 396 (1993) 779.
N. B. Wilding, Phys. Rev. E 52 (1995) 602; A. D. Bruce and N. B. Wilding, preprint cond-mat/0206111, to appear in Adv. Chem. Phys.
S. F. Edwards and P.W. Anderson, J. Phys. F5 (1975) 965.
K. Binder and A. P. Young, Rev. Mod. Phys. 56 (1986) 801.
M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
K. H. Fischer and J. A. Hertz, Spin Glasses (University Press, Cambridge, 1991).
A. P. Young (editor), Spin Glasses and Random Fields (World Scientific, Singapore, 1997).
W. Janke, B. A. Berg, and A. Billoire, Multi-Overlap Simulations of Spin Glasses, in: NIC Symposium 2001, edited by H. Rollnik and D. Wolf, John von Neumann Institute for Computing, Jülich, NIC Series, Vol. 9 (2002), pp. 301–314 [http://www.fz-juelich.de.
G. Parisi, Phys. Rev. Lett. 43 (1979) 1754.
D.S. Fisher and D.A. Huse, Phys. Rev. B 38 (1988) 386.
B. A. Berg and W. Janke, Phys. Rev. Lett. 80 (1998) 4771.
B. A. Berg, A. Billoire, and W. Janke, Phys. Rev. B 61 (2000) 12143.
B. A. Berg, U. E. Hansmann, and T. Celik, Phys. Rev. B 50 (1994) 16444.
B. A. Berg, A. Billoire, and W. Janke, Phys. Rev. E 65 (2002) 045102(R).
B. A. Berg, A. Billoire, and W. Janke, Phys. Rev. E 66 (2002) 046122.
E. Marinari and G. Parisi, Europhys. Lett. 19 (1992) 451.
A. P. Lyubartsev, A. A. Martsinovski, S. V. Shevkunov, and P. N. Vorontsov-Velyaminov, J. Chem. Phys. 96 (1992) 1776.
C. J. Geyer, in Computing Science and Statistics, Proceedings of the 23rd Symposium on the Interface, E. M. Keramidas (editor) (Interface Foundation, Fairfax, Virginia, 1991); pp. 156–163; C. J. Geyer and E. A. Thompson, J. Am. Stat. Assoc. 90 (1995) 909.
K. Hukushima and K. Nemoto, J. Phys. Soc. Japan 65 (1996) 1604.
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Janke, W. (2003). Histograms and All That. In: Dünweg, B., Landau, D.P., Milchev, A.I. (eds) Computer Simulations of Surfaces and Interfaces. NATO Science Series, vol 114. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0173-1_7
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