Abstract
In this paper, we have reviewed two complementary new approaches to improve the accuracy and efficiency of Monte Carlo computer simulations in the study of phase transitions. Substantial gains have already been achieved, and since these methods represent approaches to the problem of simulation that are still being developed, they promise further improvements in the future. In both cases, a key feature is the lifting of the restriction of thinking about computer simulations as simply “computer experiments,” and recognising that there are certain aspects of simulations that can be exploited to greatly increase their value.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
N. Metropolis, A.W. Rosenbluth. M.N. Rosenbluth, A.H. Teller, E. Teller: J. Chem. Phys. 21, 1087 (1953)
K.G. Wilson: Phys. Rev. D 10, 2445 (1974); and in Recent Developments in Gauge Theories, ed. by G. 't Hooft et al. (Plenum, New York 1980)
K. Binder: Phys. Rev. Lett. 47, 693 (1981)
K. Binder: J. Comput. Phys. 59, 1 (1985)
K. Binder (ed.): Monte Carlo Methods in Statistical Physics, Topics Curr. Phys. Vol. 7, 2nd edn. (Springer, Berlin, Heidelberg 1986); K. Binder (ed.): Applications of the Monte Carlo Method in Statistical Physics, Topics Curr. Phys., Vol. 36, 2nd edn. (Springer, Berlin, Heidelberg 1987)
J.A. McCammon, S.C. Harvey: Dynamics of Proteins and Nucleic Acids (Cambridge University Press, New York 1987), and references therein
C.H. Brooks III, M. Karplus, B.M. Pettitt: Proteins: A theoretical perspective of dynamics, structure and thermodynamics, in Advances in Chemical Physics, Vol. LXXI, ed. by I. Prigogine, S. Rice (Wiley, New York 1988)
P.C. Hohenberg, B.I. Halperin: Rev. Mod. Phys. 49, 435 (1977)
G. Parisi: In Progress in Gauge Field Theory, ed. by G. 't Hooft et al. (Plenum, New York 1984) p. 531; G.G. Batrouni G.R. Katz, A.S. Kronfeld, G.P. Lepage, B. Svetitsky, K.G. Wilson: Phys. Rev. D 32, 2736 (1985); E. Dagotto, J. Kogut: Phys. Rev. Lett. 58, 299 (1987)
J. Goodman, A.D. Sokal: Phys. Rev. Lett. 56, 1015 (1986); Phys. Rev. D 40, 2035 (1989)
D. Kandel, E. Domany, D. Ron, A. Brandt, E. Loh: Phys. Rev. Lett. 60,1591 (1988)
D. Kandel, E. Domany, A. Brandt: Phys. Rev. B 40, 330 (1988)
R. Ben-Av, D. Kandel, E. Katznelson, P.G. Lauwers, S. Solomon: J. Stat. Phys. 58,125 (1990)
D. Kandel, R. Ben-Av, E. Domany: Phys. Rev. Lett. 65, 941 (1990)
K.E. Schmidt: Phys. Rev. Lett. 51, 2175 (1983); M. Faas, H.J. Hilhorst: Physica A 135, 571 (1986); H.H. Hahn, T.S.J. Streit: Physica A 154, 108 (1988); E.P. Stoll: J. Phys. Condens. Matter 1, 6959 (1989)
M. Creutz: Phys. Rev. D 36, 515 (1987); F.R. Brown, T.J. Woch: Phys. Rev. Lett. 58, 2394 (1987); S.L. Adler: Phys. Rev. D 38, 1349 (1988)
R.H. Swendsen, J.-S. Wang: Phys. Rev. Lett. 58, 86 (1987)
P.W. Kasteleyn, C.M. Fortuin: J. Phys. Soc. Jpn. Suppl. 26s, 11 (1969); C.M. Fortuin, P.W. Kasteleyn: Physica (Utrecht) 57, 536 (1972)
D. Stauffer: Phys. Rep. 54, 1 (1979); J.W. Essam: Rep. Prog. Phys. 43, 830 (1980)
U. Wolff: Phys. Rev. Lett. 60,1461 (1988); Nucl. Phys. B 300 [FS22], 501 (1988)
F. Niedermayer: Phys. Rev. Lett. 61, 2026 (1988)
R.G. Edwards, A.D. Sokal: Phys. Rev. D 38, 2009 (1988)
U. Wolff: Phys. Rev. Lett. 62, 361 (1989)
U. Wolff: Phys. Lett. B 228, 379 (1989)
U. Wolff: Nucl. Phys. B 322, 759 (1989)
R.G. Edwards, A.D. Sokal: Phys. Rev. D 40,1374 (1989)
W. Janke: Phys. Lett. A 148, 306 (1990)
R.C. Brower, P. Tamayo: Phys. Rev. Lett. 62, 1087 (1989)
J.-S. Wang, R.H. Swendsen, R. Kotecky: Phys. Rev. Lett. 63,109 (1989)
J.-S. Wang, R.H. Swendsen, R. Kotecky: Phys. Rev. B 42, 2465 (1990)
M. Hasenbusch: Nucl. Phys. B 333, 581 (1990)
Ch. Frick, K. Jansen, P. Seuferling: Phys. Rev. Lett. 63, 2613 (1989)
M. Hasenbusch, S. Meyer: Phys. Rev. Lett. 66, 530 (1991)
W. Klein, T. Ray, P. Tamayo: Phys. Rev. Lett. 62,163 (1989)
T.S. Ray, P. Tamayo, W. Klein: Phys. Rev. A 39, 5949 (1989)
D.W. Heermann, A.N. Burkitt: Physica A 162,210 (1990)
X.-J. Li, A.D. Sokal: Phys. Rev. Lett. 63, 827 (1989); Phys. Rev. Lett. 67, 1482 (1991)
J.-S. Wang: Physica A 164, 240 (1990)
P. Tamayo, R.C. Brower, W. Klein: J. Stat. Phys. 58, 1083 (1990)
A.M. Ferrenberg, R.H. Swendsen: Phys. Rev. Lett. 61, 2635 (1988)
D.A. Chesnut, Z. W. Salsburg: J. Chem. Phys. 38, 2861 (1963)
A.M. Ferrenberg, R.H. Swendsen: Phys. Rev. Lett. 63, 1195 (1989)
A.M. Ferrenberg, R.H. Swendsen: Comput. in Phys. 101 (Sept./Oct. 1989)
R.H. Swendsen, A.M. Ferrenberg: In Computer Simulation Studies in Condensed Matter Physics II, ed. by D.P. Landau, K.K. Mon, H.-B. Schüttler, Springer Proc. Phys., Vol. 45 (Springer, Berlin, Heidelberg 1990)
C.H. Bennett: J. Comput. Phys. 22,245 (1976)
S. Huang, K.J.M. Moriarty, E. Myers, J. Potvin: In Proceedings of Supercomputing 90, p. 742 (IEEE Comput. Soc. Press, Los Alamites, CA 1990)
S. Huang, E. Myers, K.J.M. Moriarty, J. Potvin: Nucl. Phys. B, Proc. Suppl. 17, 281 (1990)
Z.W. Salsburg, J.D. Jackson, W. Fickett, W.W. Wood: J. Chem. Phys. 30, 65 (1959)
I.R. McDonald, K. Singer: Discuss. Faraday Soc. 43, 40 (1967)
J.P. Valleau, D.N. Card: J. Chem. Phys. 57, 3457 (1972)
G. Torrie, J.P. Valleau: Chem. Phys. Lett. 28, 578 (1974); J. Comput. Phys. 23, 187 (1977)
M. Falcioni, E. Marinari, M.L. Paciello, G. Parisi, B. Taglienti: Phys. Lett. 108B, 331 (1982)
E. Marinari: Nucl. Phys. B 235 [FS11], 123 (1984)
C.N. Yang, T.D. Lee: Phys. Rev. 87, 404 (1952)
G. Bhanot, S. Black, P. Carter, R. Salvador: Phys. Lett. B 183, 331 (1987)
G. Bhanot, K.M. Bitar, S. Black, P. Carter, R. Salvador: Phys. Lett. B 187, 381 (1987)
G. Bhanot, K.M. Bitar, R. Salvador: Phys. Lett. B 188, 246 (1987)
G. Bhanot, R. Salvador, S. Black, R. Toral: Phys. Rev. Lett. 59, 803 (1987)
N.A. Alves, B.A. Berg, R. Villanova: Phys. Rev. B 41, 383 (1990)
G.V. Bhanot, S. Sanielev: Phys. Rev. D 40, 3454 (1989)
M. Fukugita, M. Okawa, A. Ukawa: Phys. Rev. Lett. 63, 1768 (1989)
W. Bock, H.G. Evertz, J. Jersák, D.P. Landau, T. Neuhaus, J.L. Xu: Phys. Rev. D 41, 2573 (1990)
S. Gottlieb, W. Liu, R.L. Renken, R.L. Sugar, D. Toussaint: Phys. Rev. D 40, 2389 (1989)
R.V. Gavai, F. Karsch: Phys. Lett. B 233, 417 (1989)
M. Fukugita, H. Mine, M. Okawa, A. Ukawa: J. Stat. Phys. 59,1397 (1990)
W. Janke, H. Kleinert: Phys. Lett. A 140, 513 (1989)
N. Caticha, J. Chahine, H.R. Drugowich de Félicio: Phys. Rev. A 40, 7431 (1989)
J. Chahine, H.R. Drugowich de Félicio, N. Caticha: Phys. Lett. A 139, 360 (1989)
E.P. Münger, M.A. Novotny: Phys. Rev. B 43, 5573 (l991)
F. Mallezie: Phys. Rev. B 41, 4475 (1990)
A.M. Ferrenberg, D.P. Landau: Phys. Rev. B 44, 5081 (1991)
H. Müller-Krumbhaar, K. Binder: J. Stat. Phys. 8,1 (1973)
A. Coniglio, W. Klein: J. Phys. A 13, 2775 (1980)
C.-K. Hu: Phys. Rev. B 29, 5103, 5109 (1984)
J. Hoshen, R. Kopelman: Phys. Rev. B 14, 3438 (1976)
C.F. Baillie, P.D. Coddington: Concurrency: Practice and Experience 3, 129 (1991)
H. Mino: Comput. Phys. Commun. 66, 25 (1991)
A.N. Burkitt, D.W. heermann: Parallel Comput. 13, 345 (1990)
C.-K. Hu, K.-S. Mak: Phys. Rev. B 40, 5007 (1989)
M.D. De Meo, D.W. Heermann, K. Binder: J. Stat. Phys. 60, 585 (1990)
F. Niedermayer: Phys. Lett. B 237, 473 (1990)
M. Sweeny: Phys. Rev. B 27, 4445 (1983)
M. Hasenbusch, S. Meyer: Phys. Lett. B 241, 238 (1990)
J.-S. Wang, W. Selke, VLS. Dotsenko, V.B. Andreichenko, Europhys. Lett. 11, 301 (1990); Physica A 164, 221 (1990)
J.-S. Wang and D. Chowdhury: J. de Phys. 50, 2905 (1989); J.-S. Wang, M. Wbhlert, H. Mühlenbein, D. Chowdhury: Physica A 166, 173 (1990)
Z. Alexandrowicz: Physica A 160, 310 (1989)
J.-S. Wang: Physica A 161, 249 (1989)
A. Coniglio, F. Liberto, G. Monroy, F. Peruggi: J. Phys. A: Math. Gen. 22, L837 (1989)
J.-S. Wang, D. Stauffer: Z. Phys. B 78, 145 (1990)
A.N. Burkitt, D.W. Heermann: Europhys. Lett. 10, 207 (1989)
D. Stauffer: Physica A 102, 27 (1989)
T.S. Ray, P. Tamayo: J. Stat. Phys. 60, 851 (1990)
T.S. Ray, J.-S. Wang: Physica A 167, 580 (1990)
J.-S. Wang, R.H. Swendsen: Physica A 167, 565 (1990)
LA. Chen, C.-K. Hu, K.-S. Mak: Comput. Phys. Commun. 66, 377 (1991)
R.H. Swendsen, J.-S. Wang: Phys. Rev. Lett. 57, 2607 (1986)
J.-S. Wang, R.H. Swendsen: Phys. Rev. B 38, 4840 (1988)
J.-S. Wang, R.H. Swendsen: Phys. Rev. B 38, 9086 (1988)
J.-S. Wang, R.H. Swendsen: Phys. Rev. B 37, 7745 (1988)
R.N. Bhatt, A.P. Young: Phys. Rev. Lett. 54, 924, (l985)
A.T. Ogielski, I. Morgenstern: Phys. Rev. Lett. 54, 928 (1985)
A.T. Ogielski: Phys. Rev. B 32, 7384 (1985)
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag
About this chapter
Cite this chapter
Swendsen, R.H., Wang, JS., Ferrenberg, A.M. (1992). New monte carlo methods for improved efficiency of computer simulations in statistical mechanics. In: Binder, K. (eds) The Monte Carlo Method in Condensed Matter Physics. Topics in Applied Physics, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60174-0_4
Download citation
DOI: https://doi.org/10.1007/3-540-60174-0_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60174-6
Online ISBN: 978-3-540-44664-4
eBook Packages: Springer Book Archive