Abstract
This chapter tries to summarize some of the general progress which has been made during the last decade in the understanding of the Monte Carlo method in statistical physics and in its efficient implementation; but it will also point out some problems which still remain to be solved. In fact, there has been an enormously growing interest in the use of this method, and even a brief review of its recent applications fills a whole book [10.11; thus, the present chapter will not attempt to cover these applications in complete detail, but rather attention will be focused on a few highlights which serve to illustrate some general points.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
K. Binder (ed.): Applications of the Monte Carlo Method in Statistical Physics, Topics Current Phys., Vo1.36 (Springer, Berlin, Heidelberg 1984)
For recent reviews, see C. Rebbi: In /Ref.10.1, Chap.9/; M. Creutz, L. Jacobs, C. Rebbi: Phys. Repts. 95C, 203 (1983); B. Berg: In Proc. Cargèse lectures 1983, to be published
K. Binder, D. Stauffer: In /Ref.10.1, Chap. 1/
K. Binder: Adv. Phys. 23, 1 (1974); and in Phase Transitions and Critical Phenomena 5b, 1 (Academic, New York 1976]
K. Binder: J. Comp. Phys. 59, 1 (1985)
K. Binder: Ferroelectrics, in press
V. Privman, M.E. Fisher: J. Stat. Phys. 33, 385 (1983)
K. Binder, D.P. Landau: Phys. Rev. B30, 1477 (1984)
K. Binder, M. Nauenberg, V. Privman, A.P. Young: Phys. Rev. B31, 1498 (1985)
E. Brezin, J. Zinn-Justin: Nucl. Phys. B257 /FS14/, 867 (1985) J. Rudnick, H. Guo, D. Jasnow: J. Stat. Phys. 41, 353 (1985)
V. Privman, M.E. Fisher: Phys. Rev. B32, 447 (1985)
M.S.S. Challa, D.P. Landau, K. Binder: preprint
A. Nemirovsky, K.F. Freed: Phys. Rev. B31, 3161 (1985); J. Phys. A18, L319 (1985); and preprints; E. Eisenriegler: preprints
J. Rudnick, G. Gaspari, V. Privman: Phys.Rev. B32, 7594 (1985)
For general introductions to this field see: F. Family, D.P. Landau (eds.): Kinetics of Aggregation and Gelation (Elsevier, New York 1984); R. Pynn, T. Skjeltorg (eds.): Scaling Phenomena in Disordered Systems (Plenum, New York 1985); R. Jullien, M. Kolb, H.Herrmann, J.Vannimenus: J.Stat.Phys. 39, 241 (1985)
K.E. Schmidt, M.H. Kalos: In /Ref.10.1,Chap.4/
M.H. Kalos (ed.): Monte Carlo Methods in Quantum Problems (Reidel, Dordrecht, Holland 1985]
H. De Raedt, A. Lagendijk: Phys. Repts. 127, 235 (1985)
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller: J. Chem. Phys. 21, 1987 (1953)
H.E. Müser: Ferroelectrics 39 1099 (1981); H.D. Maier, H.E. Müser, J. Peterson: Z. Phys. B46, 251 (1982)
P. Bak: Phys. Today 36, No. 12, 25 (1983)
A. Hooghland, J. Spaa, B. Selman, A. Compagner: J. Comput. Phys. 51, 250 (1983)
R.B. Pearson, J.L. Richardson, D. Toussaint: J.Comput.Phys. 51, 243 (1983)
J.H. Condon, A.T. Ogielski: Rev. Sci. Instr. 56, 1691 (1985)
N.H. Christ, A.E. Terrano: Columbia University preprint CU-TP-261
A.F. Bakker, C. Bruin, F. van Dieren, H.J. Hilhorst: Phys. Lett. A93, 67 (1982)
A.F. Bakker, C. Bruin, H.J. Hilhorst: Phys. Rev. Lett. 52, 449 (1984)
R. Zorn, H.J. Herrmann, C. Rebbi: Comp. Phys. Commun. 23, 337 (1981); L. Jacobs, C. Rebbi: J. Comput. Phys. 41, 203 (1981)
C. Kalle, V. Winkelmann: J. Stat. Phys. 28, 639 (1982)
K. Binder, D.P. Landau: Phys. Rev. Lett. 52, 318 (1984)
W. Selke, M.E. Fisher: Z. Phys. B40, 71 (1980); J. Magn. Mag. Mat. 15–18, 403 (1980)
W. Selke: Z. Phys. B43, 335 (1981)
H.J. Hilhorst: priv. commun.
M.E. Fisher: Rev. Mod. Phys. 46, 597 (1974); and in Critical Phenomena, ed. by M.S. Green (Academic, New York 1971) p. 1
M.N. Barber, R.B. Pearson, J.L. Richardson, D. Toussaint: Phys. Rev.B32, 1720 (1985)
R.B. Pearson: Phys. Repts. 103, 185 (1985)
K. Binder, M. Nauenberg, V. Privman, A.P. Young:Phys.Rev.B31, 1499 (1985)
A. Hoogland, A. Compagner, H.W.J. Blöte: Physica A132, 593 (l985)
R.C. Tausworthe: Math. Comp. 19, 291 (1965)
N. Zierler: Inform. Control. 15, 67 (1969)
J.P.R. Tootill, W.D. Robinson, A.G. Adams: J.Ass.Computing Machinery 18, 381 (1971)
S. Kirkpatrick, E.P. Stoll: J. Comput. Phys. 40, 517 (1981)
A.T. Ogielski, I. Morgenstern: Phys. Rev. Lett. 54, 928 (1985); see also A.T. Ogielski, D.A. Huse: Preprint, for recent work on dilute antiferromagnets in a field
A.T. Ogielski: Phys. Rev. B32, 7384 (1985)
R.N. Bhatt, A.P. Young: Phys. Rev. Lett. 54, 924 (1985)
K. Binder, K. Schröder: Phys. Rev. B14, 2142 (1976); Solid State Commun. 18, 1361 (1976)
K. Binder: J. Phys. 39, C6–1527 (1978)
K. Binder, D. Stauffer: In /Ref.10.1, Chap.8/and Chapter 8 of the present book
K. Binder, W. Kinzel: In Heidelberg Colloquium on Spin Glasses, ed. by J.L. van Hemmen, I. Morgenstern (Springer, Berlin, Heidelberg 1983) p.279
K. Binder, A.P. Young: Rev. Mod. Phys., to be published
R. Kretschmer, K. Binder: Z. Phys. B34, 375 (1979)
R.W. Walstedt, L.R. Walker: Phys. Rev. Lett. 47, 1624 (1981)
D. Sherrington, S. Kirkpatrick: Phys. Rev. Lett. 35, 1792 (1975)
A.P. Young: Phys. Rev. Lett. 51, 1206 (1983); W. Kinzel: preprint
R.N. Bhatt, A.P. Young: preprint
A. Baumgärtner: J. Phys. Lett. (Paris) 45, L-515 (1984)
D. Barkai, M. Creutz, K.J. Moriarty: Nucl. Phys. B225, /FS 9/, 156 (1983) see also D. Barkai, K.J.M. Moriarty: Comp. Phys. Commun. 25, 57 (1982)
A.D. Kennedy, J. Kuti, S. Meyer, B.J. Pendleton: Phys. Rev. Lett. 54, 87 (1985) B. Berg, A. Billoire, S. Meyer, C. Panagiotakopoulos: Phys. Lett. B133, 359 (1983)
G.S. Pawley, R.H. Swendsen, D.J. Wallace, K.G. Wilson: Phys. Rev. B29, 4030 (1984)
S. Wansleben, J.G. Zabolitzky, C. Kalle: J. Stat. Phys. 37, 271 (1984)
C. Kalle: J. Phys. A17, L801 (1984)
M. Kikuchi, Y. Okabe: Progr. Theor. Phys. 74, 458 (1985)
S.F. Reddaway, D.M. Scott, K.A. Smith: Comp. Phys. Commun. 37, (1985)
W. Oed: Appl. Informatics 7, 358 (1982)
M. Creutz: Phys. Rev. Lett. 50, 1411 (1983)
K.A. Smith, S.F. Reddaway, D.M. Scott: Comp. Phys. Commun. 37, (1985)
J.C. Le Guillou, J. Zinn-Justin: Phys. Rev. B21., 3976 (1980)
H.W.J. Blöte, R.H. Swendsen: Phys. Rev. B20, 2077 (1979); P.S. Sahni, J.R. Banavar: Phys. Lett. A85, 56 (1981)
K. Binder: Phys. Rev. Lett. 47, 693 (1981); Z. Phys. B43, 119 (1981)
P.C. Hohenberg, B.I. Halperin: Rev. Mod. Phys. 49, 435 (1977)
H. Müller-Krumbhaar, K. Binder: J. Stat. Phys. 8, 1 (1973)
E. Stoll, K. Binder, T. Schneider: Phys. Rev. B8, 3266 (1973)
B.K. Chakrabarty, H.G. Baumgaertel, D. Stauffer: Z. Phys. B44, 333 (1981)
J. Tobochnik, S. Sarker, R. Cordery: Phys. Rev. Lett. 46, 1417 (1981); M.C. Yalabik, J.D. Gunton: Phys. Rev. B25, 534 (1982); N. Jan, L.L. Moseley, D. Stauffer: J. Stat. Phys. 33, 1 (1983)
K. Binder: J. Stat. Phys. 24, 69 (1981); J. Tobochnik, A. Jayaprakash: Phys. Rev. B25, 4891 (1972); M. Aydin, M.C. Yalabik: J. Phys. A17, 253l (l984)
A. Sadiq, K. Binder: J. Stat. Phys. 35, 517 (1984)
E. Brezin, J.C. Le Guillou, J. Zinn-Justin: Phys. Lett. A47, 285 (1974)
M. Kikuchi, Y. Okabe: Phys. Rev. Lett. 55, 1220 (1985)
K. Binder: Phys. Rev. A25, 1699 (1982)
W. Schweika: Dissertation, RW TH Aachen (1985) unpublished
M. Suzuki: Progr. Theor. Phys. 58, 1142 (1977)
M.N. Barber: In Phase Transitions and Critical Phenomena, Vol. 8, ed. by C. Domb, J.L. Lebowitz (Academic, London 1983) Chap. 2
D.P. Landau: Phys. Rev. B13, 2997 (1976); B14, 255 (1976)
K. Binder, D.P. Landau: Phys. Rev. B21, 1941 (1980)
D.P. Landau: Phys. Rev. B21, 1285 (1980)
S. Miyashita, H. Takano: Progr. Theor. Phys. 73, 1122 (1985)
D.P. Landau, K. Binder: Phys. Rev. B31, 5946 (1985)
A. Milchev, D.W. Heermann, K. Binder: preprint
M.N. Barber, W. Selke: J.Phys. A15, L617 (1982)
R.H. Swendsen, S. Krinsky: Phys. Rev. Lett. 43, 177 (1979)
J. Oitmaa: J. Phys. A14, 1159 (1981)
M.P, Nightingale: Phys. Lett. A59, 486 (1977)
M. Nauenberg, B. Nienhuis: Phys. Rev.Lett. 33, 944 (1974)
K. Binder, W. Kinzel, D.P. Landau: Surf. Sci. 117, 232 (1982)
D.P. Landau: J.Magn. Magn. Mat. 31–34, 11 (1983)
D.P. Landau: J. Appl. Phys. 42, 1284 (1971)
J.M. Kosterlitz, D.J. Thouless: J. Phys. C6, 1181 (1973)
C.S.S. Murty, D.P. Landau: preprint
C.S.S. Murty, D.P. Landau: J. Appl. Phys. 55, 2429 (1984)
K. Binder: Z. Phys. B61, 13 (1985)
Y. Imry: Phys. Rev. B21, 2042 (1980)
S.-K. Ma: Phys. Rev. Lett. 37, 461 (1976)
R.H. Swendsen: Phys. Rev. Lett. 42, 859 (1979)
R.H. Swendsen: Phys. Rev. Lett. 52, 1165 (1984)
R.H. Swendsen: In Phase Transitions, Cargèse 1980, ed. by M. Levy, J.C. Le Guillou, J. Zinn-Justin (Plenum, New York 1982) p.395
R.H. Swendsen: In Real-Space Renormalization, ed. by Th.W. Burkhardt, J.M.J. van Leeuwen, Topics Current Phys., Vol. 30 (Springer, Berlin, Heidelberg 1982) p.57
R.H. Swendsen: J. Stat. Phys. 34, 963 (1984)
Th. Niemeijer, J.M.J. van Leeuwen: In Phase Transitions and Critical Phenomena, Vol. 6, ed. by C. Domb, M.S. Green (Academic, New York 1976) T.W. Burkhardt, J.M.J. Van Leeuwen (eds.): Real Space Renormalization, Topics Current Phys. Vol. 30 (Springer, Berlin, Heidelberg 1982)
D.P. Landau, R.H. Swendsen: Phys. Rev. Lett. 46, 1437 (1981); see also K.G. Wilson: In Physics of Defects, ed. by R. Balian, M.Kléman, J.-P. Poirier (North-Holland, Amsterdam 1982)
M. Creutz: Phys. Rev. D23, 1815 (1981); see also S. Shenker, J. Tobochnik: Phys. Rev. B22, 4462 (1980) for a related approach for the case of the d=2 Heisenberg ferromagnet
J. Tobochnik, S. Sarker, R. Cordery: Phys. Rev. Lett. 46, 1417 (1981); J. Tobochnik, C. Jayaprakash: Phys. Rev. B25, 4893 (1982); M. Aydin, M.C. Yalabik: J. Phys. A17, 667, 2531 (1984)
J. Vinals, M. Grant, M. San Miguel, J.D. Gunton, E.T. Gawlinski: Phys. Rev. Lett. 54, 1264 (1985); J. Vinals, J.D. Gunton: preprint
M. Creutz, L.Jacobs, C. Rebbi: Phys. Rev. D20, 1915 (1979)
K. Wilson: Phys. Rev. D10, 2445 (1972)
B.Berg, S. Meyer, I. Montvay, K. Symanzik: Phys. Rev. Lett. B126, 467 (1983)
C.B. Lang, C. Rebbi, P. Salomonson, B.S. Shargerstam: Phys. Rev. D21, 1006 (1980)
B.B. Mandelbrot: Fractals: Form, Chance and Dimension (Freeman, San Francisco 1977)
L. Pietronero, E. Tosatti (eds.): Fractals in Physics, to be published
T.A. Witten, Jr., L.M. Sander: Phys. Rev. Lett. 47, 1400 (1981); Phys. Rev. B27, 5686 (1983); P.A. Meakin: Phys. Rev. B24, 604, 1495 (1983)
I. Majid, N. Jan, A. Coniglio, H.E. Stanley: In Kinetics of Aggregation and Gelation, ed. by F. Family, D.P. Landay (North Holland, Amsterdam 1984) p.51; J.W. Lyklema, K. Kremer: ibid. p.241; I. Majid, N. Jan, A. Coniglio, H.E. Stanley: Phys. Rev. Lett. 52, 1257 (1984); J.W. Lyklema, K. Kremer: J. Phys. A17, L 691 (1984); S. Hemmer, P.C. Hemmer: J. Chem. Phys. 81, 584 (1984)
L. Peliti: J. Phys. (Paris) Lett. 45, 45 (1984); K. Kremer, J.W. Lyklema: Phys. Rev. Lett. 55, 2091 (1985); J.W. Lyklema, K. Kremer: J. Phys. A, in print; J.W. Lyklema, K. Kremer: Phys. Rev. B31, 3182 (1985)
K. Kremer, J.W. Lyklema: Phys. Rev. Lett. 54, 267 (1985); J. Phys. A18, 1515 (1985)
J.W. Lyklema: J. Phys. A18 L617 (1985)
J.W. Lyklema, C. Evertsz: In /10.118/
J.W. Lyklema: In /10.118/L. Peliti, L. Pietronero: La Rivista del nuovo Cimento, in press
K.W. Kehr, K. Binder: In /Ref. 10.1, Chap.6/
G.E. Murch: Atomic Diffusion Theory in Highly Defective Solids (Trans Tech. House, Adermannsdorf 1980)
A. Baumgärtner: In /Ref.10.1, Chap.5/
A. Baumgärtner: Ann. Rev. Phys. Chem. 35, 419 (1984)
P.G. de Gennes: Scaling Concepts in Polymer Physics (Cornell U. Press, Ithaca, NY 1979)
J.W. Halley, H. Nakanishi: Phys. Rev. Lett. 55, 551 (1985)
M. Muthukumar: Phys. Rev. Lett. 50, 893 (1983T; T. Witten, M. Nauenberg: unpublished
H. Gould, F. Family, H.E. Stanley: Phys. Rev. Lett. 50, 686 (1983); M. Tokuyama, K. Kawasaki: Phys. Lett. A100, 337 (19847; H.G.E. Hentschel: Phys. Rev. Lett. 52, 212 (1984)
D.A. Weitz, M. Oliveria: Phys. Rev. Lett. 52, 1433 (1984)
L.A. Turkevich, H. Scher: Phys. Rev. Lett. 55, 1026 (1985)
M. Kolb, R. Botet, R. Jullien: Phys. Rev. Lett. 51, 1123 (1983); R. Botet, R. Jullien, M. Kolb: J. Phys. A17, 175-(1985)
A. Sadiq, K. Binder: J. Stat. Phys. 35, 617 (1984)
K. Binder, D.W. Heermann: In Scaling Phenomena in Disordered Systems, ed. by R. Pynn, T. Skjeltorp (Plenum, New York 1985)
D.C. Handscomb: Proc. Camb. Phil. Soc. 58, 594 (1962); Proc. Camb. Phil. Soc. 60, 115 (1964)
J.W. Lyklema: Phys. Rev. B27, 3108 (1983)
J.W. Lyklema: Phys. Rev. Lett. 49, 88 (1982)
S. Chakravarty, D.B. Stein: Phys. Rev. Lett. 49, 582 (1982)
H.F. Trotter: Proc. Am. Math. Soc. 10, 545 (1959)
M. Suzuki: Progr. Theor. Phys. 56, 1454 (1976); Commun. Math. Phys. 51, 183 (1976)
M. Suzuki, S. Miyashita, A. Kuroda: Progr. Theor. Phys. 58, 1377 (1977)
J.J. Cullen, D.P. Landau: Phys. Rev. B27, 297 (1983)
M. Barma, B.S. Shastry: Phys. Rev. B18, 3351 (1978)
H. De Raedt, B. De Raedt: Phys. Rev. A28, 3575 (1983); H. De Raedt, A. Lagendjk: Phys. Rev. Lett. 46, 77 (1981); J.Stat.Phys. 27, 731 (1982); Phys. Rev. B24, 463 (1981); Phys. Rev. Lett. 49, 1552 (1982); Phys. Rev. B27, 921, 6097 (1983); B30, 1671 (1984); H. De Raedt, B. De Raedt, A. Lagendijk: Z. Phys. B57, 209 (1984)
B. De Raedt, H. De Raedt: Phys. Rev. Lett. 50, 1926 (1983); Phys. Rev. B29, 5352 (1985)
R.P. Feynman, A.R. Hibbs: Quantum Mechanics and Path Integrals (McGraw-Hill, New York 1976)
L. Jacobs, J.V. José, M.A. Novotny: Phys. Rev. Lett. 53, 2177 (1984)
J.E. Hirsch, D.J. Scalapino, R.L. Sugar, R. Blancenbecler: Phys.Rev. Lett. 47, 1628 (1981); Phys. Rev. B26, 5033 (1982); see also J.A. Barker: J. Chem. Phys. 70, 2914 (1979); D. Chandler, P.G. Wolynes: J. Chem. Phys. 74, 4078 (1981); R.M. Stratt: J. Chem. Phys. 75, 1347 (1982)
For a review, see J.E. Hirsch: In /10.17/
M. Takahashi, M. Imada: J. Phys. Soc. Jpn 53, 963 (1984); J. Phys. Soc. Jpn 53, 3765, 3871 (1984)
J.E. Hirsch, E. Fradkin: Phys. Rev. Lett. 49, 402 (1982); Phys. Rev. B27, 1680, 4302 (1983)
J.E. Hirsch: Phys. Rev. B28, 4059 (1983); D.J. Scalapino, R.L. Sugar, W.D. Toussaint: Phys. Rev. B29, 5253 (1984); J.E. Hirsch: Phys. Rev. Lett. 51, 296 (1983); J.E. Hirsch, D.J. Scalapino: Phys. Rev. Lett. 50, 1168 (1983); Phys. Rev. B27, 7169 (1983)
J.E. Hirsch, M. Grabowski: Phys. Rev. Lett. 52, 1713 (1984); D.K. Campbell, T.A. De Grand, S. Mazumdar: Phys. Rev. Lett. 52, 1717 (1984)
J. Kuti: Phys. Rev. Lett. 49, 183 (1982)
D.L. Freeman, J.D. Doll: J. Chem. Phys. 80, 2239, 5709 (1984); J.D. Doll, R.D. Coalson, D.L. Freeman: Phys. Rev. Lett. 55, 1 (1985); J.D. Doll, L.E. Myers: J. Chem. Phys. 71, 2880 (1979)
D. Thirumalai, B.J. Berne: J. Chem. Phys. 79, 5029 (1983); E.C. Behrman, G.A. Jongeward, P.G. Wolynes: J. Chem. Phys. 79, 6227 (1983)
J.D. Doll: J. Chem. Phys. 81, 3536 (1984)
H.B. Schüttler, D.J. Scalapino: Phys. Rev. Lett. 55, 1204 (1985); J.E. Hirsch, J.R. Schrieffer: Phys. Rev. B28, 5353 (1983)
A. Baumgärtner: In /Ref.10.1, Chap.5/; Ann. Rev. Phys. Chem. 35, 419 (1984); J. Phys. A17, L971 (1984); J. Chem. Phys. 81, 1484 (1984)
K. Binder: Phys. Rev. Lett. 45, 811 (1980); Z. Phys. B45, 61 (1981); K. Binder, J.L. Lebowitz, M.K. Phani, M.H. Kalos: Acta Metall. 29, 1655 (1981); U. Gahn: J. Phys. Chem. Solids 43, 977 (1982); R.A. Bond, D.K. Ross: J. Phys. F12, 597 (1982); J.L. Lebowitz, M.K. Phani, D. Styer: J. Stat. Phys. 38, 413 (1985); K. Binder: preprint
V. Gerold, J. Kern: preprint
T.L. Polgreen: Phys. Rev. B29, 1468 (1984); H. Meirovitch: J. Stat. Phys. 30, 681 (1983); J. Phys. A16, 839 (1983); Phys. Rev. B30, 2866 (1984)
A.P. Young, M. Nauenberg: Phys. Rev. Lett. 54, 2429 (1985)
D.W. Heermann: Introduction to Computer Simulation Methods in Theoretical Physics (Springer, Berlin, Heidelberg 1986)
D.P. Landau, K. Binder: An Introduction to Monte Carlo Simulation Methods in Physics, in preparation
W. Smith (ed.): Information Quarterly for Computer Simulations of Condensed Phases (Sci. Eng. Res. Council, Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, England; 1st issue: 1981)
T. Filk, M. Marcu, K. Fredenhagen: DESY preprint 85–098
S. Wolfram: Phys. Rev. Lett. 55, 449 (1985)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Binder, K. (1986). Recent Trends in the Development and Application of the Monte Carlo Method. In: Binder, K. (eds) Monte Carlo Methods in Statistical Physics. Topics in Current Physics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82803-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-82803-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16514-9
Online ISBN: 978-3-642-82803-4
eBook Packages: Springer Book Archive