Skip to main content
SpringerLink
Log in

Some Important Recent Developments of the Monte Carlo Methodology

  • Chapter
Monte Carlo Simulation in Statistical Physics

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 80))

  • 560 Accesses

Abstract

Roughly at the time (1987) when the manuscript for the first three chapters of the present book was completed, several breakthroughs occurred. They had a profound influence on the scope of Monte Carlo simulations in statistical physics, particularly for the study of phase transitions in lattice models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.H. Swendsen, J.-S. Wang: Phys. Rev. Lett. 58, 86 (1987)

    ADS  Google Scholar 

  2. U. Wolff: Phys. Rev. Lett. 60, 1461 (1988)

    MathSciNet  ADS  Google Scholar 

  3. U. Wolff: Nucl. Phys. B 300, 501 (1988)

    ADS  Google Scholar 

  4. F. Niedermayer: Phys. Rev. Lett. 61, 2026 (1988)

    ADS  Google Scholar 

  5. R.G. Edwards, A.D. Sokal: Phys. Rev. D 38, 2009 (1988)

    MathSciNet  ADS  Google Scholar 

  6. R.G. Edwards, A.D. Sokal: Phys. Rev. D 40, 1374 (1989)

    ADS  Google Scholar 

  7. U. Wolff: Phys. Rev. Lett. 62, 361 (1989)

    ADS  Google Scholar 

  8. U. Wolff: Phys. Lett. B 228, 379 (1989)

    ADS  Google Scholar 

  9. U. Wolff: Nucl. Phys. B 322, 759 (1989)

    ADS  Google Scholar 

  10. W. Klein, T.S. Ray, P. Tamayo: Phys. Rev. Lett. 62, 163 (1989)

    ADS  Google Scholar 

  11. T.S. Ray, P. Tamayo, W. Klein: Phys. Rev. A 39, 5949 (1989)

    ADS  Google Scholar 

  12. Ch. Frick, K. Jansen, P. Seuferling: Phys. Rev. Lett. 63, 2613 (1989)

    ADS  Google Scholar 

  13. X.-J. Li, A.D. Sokal: Phys. Rev. Lett. 63, 827 (1989)

    ADS  Google Scholar 

  14. C.-K. Hu, K.-S. Mak: Phys. Rev. B 40, 5007 (1989)

    ADS  Google Scholar 

  15. J.-S. Wang, D. Chowdhury: J. Phys. (Paris) 50, 2905 (1989)

    Google Scholar 

  16. J.-S. Wang: Physica A 161, 249 (1989)

    ADS  Google Scholar 

  17. Z. Alexandrowicz: Physica A 160, 310 (1989)

    ADS  Google Scholar 

  18. D. Stauffer: Physica A 162, 27 (1989)

    ADS  Google Scholar 

  19. A.N. Burkitt, D.W. Heermann: Europhys. Lett. 10, 207 (1989)

    ADS  Google Scholar 

  20. A. Coniglio, F. Liberto, G. Monroy, F. Peruggi: J. Phys. A: Math. Gen. 22, L837 (1989)

    ADS  Google Scholar 

  21. R.C. Brower, P. Tamayo: Phys. Rev. Lett. 62, 1087 (1989)

    ADS  Google Scholar 

  22. J.-S. Wang, R.H. Swendsen, R. Kotecky: Phys. Rev. Lett. 63, 109 (1989)

    ADS  Google Scholar 

  23. J.-S. Wang, R.H. Swensen, R. Kotecky: Phys. Rev. B 42, 2465 (1990)

    ADS  Google Scholar 

  24. W. Janke: Phys. Lett. A 148, 306 (1990)

    MathSciNet  ADS  Google Scholar 

  25. M. D’Onorio de Meo, D.W. Heermann, K. Binder: J. Stat. Phys. 60, 585 (1990)

    ADS  Google Scholar 

  26. J.-S. Wang, D. Stauffer: Z. Physik B 78, 145 (1990)

    ADS  Google Scholar 

  27. T.S. Ray, P. Tamayo: J. Stat. Phys. 60, 851 (1990)

    ADS  Google Scholar 

  28. T.S. Ray, J.-S. Wang: Physica A 167, 580 (1990)

    ADS  Google Scholar 

  29. J.-S. Wang, R.H. Swendsen: Physica A 167, 565 (1990)

    MathSciNet  ADS  Google Scholar 

  30. D. Kandel, R. Ben-Av, E. Domany: Phys. Rev. Lett. 65, 941 (1990)

    ADS  Google Scholar 

  31. R. Ben-Av, D. Kandel, E. Katznelson, P.G. Lauwers: J. Stat. Phys. 58, 125 (1990)

    MathSciNet  ADS  Google Scholar 

  32. R.C. Brower, S. Huang: Phys. Rev. D 62, 708 (1990)

    ADS  Google Scholar 

  33. J.-S. Wang, M. Wöhlert, H. Mühlenbein, D. Chowdhury: Physica A 166, 173 (1990)

    ADS  Google Scholar 

  34. J.-S. Wang, W. Selke, V.S. Dotsenko, V.B. Andreichenko: Europhys. Lett. 11, 301 (1930); Physica A 164, 221 (1990)

    ADS  Google Scholar 

  35. F. Niedermayer: Phys. Lett. B 237, 473 (1990)

    ADS  Google Scholar 

  36. D.W. Heermann, A.N. Burkitt: Physica A 162, 210 (1990)

    ADS  Google Scholar 

  37. J.-S. Wang: Physica A 164, 240 (1990)

    ADS  Google Scholar 

  38. P. lamayo, R.C. Brower, W. Klein: J. Stat. Phys. 58, 1083 (1990)

    ADS  Google Scholar 

  39. M. Hasenbusch: Nucl. Phys. B 333, 581 (1990)

    ADS  Google Scholar 

  40. M. Hasenbusch, S. Meyer: Phys. Lett. B241, 238 (1990)

    Google Scholar 

  41. M. Hasenbusch, S. Meyer: Phys. Rev. Lett. 66, 530 (1991)

    ADS  Google Scholar 

  42. X.-J. Li, A.D. Sokal: Phys. Rev. Lett. 67, 1482 (1991)

    MathSciNet  ADS  MATH  Google Scholar 

  43. L.-J. Chen, C.-K. Hu, K.-S. Mak: Comput. Phys. Commun. 66, 377 (1991)

    MathSciNet  ADS  MATH  Google Scholar 

  44. D. Kandel, E. Domany: Phys. Rev. B 43, 8539 (1991)

    ADS  Google Scholar 

  45. R.C. Brower, P. Tamayo: Physica A 193, 314 (1992)

    ADS  Google Scholar 

  46. R.H. Swendsen, J.-S. Wang, A.M. Ferrenberg: In The Monte Carlo Method in Condensed Matter Physics, ed. by K. Binder, 2nd edn., Topics Appl. Phys., Vol. 71 (Springer, Berlin, Heidelberg 1995) Chap. 4

    Google Scholar 

  47. U. Wolff: In Computational Methods in Field Theory, ed. by H. Gausterer, C.B. Lang (Springer, Berlin, Heidelberg 1992) p. 125

    Google Scholar 

  48. A.D. Sokal: In Quantum Fields on the Computer, ed. M. Creutz (World Scientific, Singapore 1992) p. 211

    Google Scholar 

  49. H.G. Evertz, M. Marcu, G. Lana: Phys. Rev. Lett. 70, 875 (1993);

    ADS  Google Scholar 

  50. S. Wiseman, E. Domany: Phys. Rev. E 48, 4080 (1983)

    ADS  Google Scholar 

  51. P.D. Caddington, L. Han: Phys. Rev. B 50, 3058 (1994)

    ADS  Google Scholar 

  52. E. Luijten, H.W.J. Blöte: Int’l J. Mod. Phys. C 6, 359 (1995); Phys. Rev. Lett. 76, 1557, 3662 (1996)

    ADS  Google Scholar 

  53. J. Machta, Y.S. Choi, A. Lucke, T. Schweizer, L.V. Chayes: Phys. Rev. Lett. 75, 2792 (1995)

    ADS  MATH  Google Scholar 

  54. T.B. Liverpool, S.C. Glotzer: Phys. Rev. E 53, R 4255 (1996)

    ADS  Google Scholar 

  55. J.E. Gubernatis, N. Kawashima: In Monte Carlo and Molecular Dynamics of Condensed Matter Systems, ed. by K. Binder, G. Ciccotti (Società Italiana di Fisica, Bologna 1996) p. 518;

    Google Scholar 

  56. N. Kawashima, J.E. Gubernatis: Phys. Rev. E 51, 1547 (1995)

    ADS  Google Scholar 

  57. P.W. Kasteleyn, F.M. Fortuin: J. Phys. Soc. J.n. 26, Suppl., 11 (1969);

    ADS  Google Scholar 

  58. C.M. Fortuin, P.W. Kasteleyn: Physica 57, 536 (1972)

    MathSciNet  ADS  Google Scholar 

  59. J. Goodman, A.D. Sokal: Phys. Rev. Lett. 56, 1015 (1986); Phys. Rev. D40, 2035 (1989)

    ADS  Google Scholar 

  60. D. Kandel, E. Domany, A. Brandt: Phys. Rev. B 40, 330 (1989)

    ADS  Google Scholar 

  61. M. Hasenbusch, S. Meyer, G. Mack: Nucl. Phys. B (Proc. Suppl.) 20, 110 (1991)

    ADS  Google Scholar 

  62. W. Janke, T. Sauer: Chem. Phys. Lett. 201, 499 (1993)

    ADS  Google Scholar 

  63. W. Janke: In Computer Simulation Studies in Condensed Matter Physics VII, ed. by D.P. Landau, K.K. Mon, H.-B. Schüttler, Springer Proc. Phys. 78, 29 (Springer, Berlin, Heidelberg 1994)

    Google Scholar 

  64. W. Janke, T. Sauer: J. Stat. Phys. 78, 75 (1995)

    Google Scholar 

  65. G.A. Baker, Jr., N. Kawashima: Phys. Rev. Lett. 75, 994 (1995)

    ADS  Google Scholar 

  66. A.M. Ferrenberg, R.H. Swendsen: Phys. Rev. Lett. 61, 2635 (1988)

    ADS  Google Scholar 

  67. Z.W. Salsburg, D. Jacobson, W. Fickett, W.W. Wood: J. Chem. Phys. 30, 65 (1959)

    ADS  Google Scholar 

  68. D.A. Chestnut, Z.W. Salsburg: J. Chem. Phys. 38, 2861 (1963);

    ADS  Google Scholar 

  69. I.R. McDonald, K. Singer: Discuss. Faraday Soc. 43, 40 (1967)

    Google Scholar 

  70. A.M. Ferrenberg, R.H. Swendsen: Phys. Rev. Lett. 63, 1195 (1989)

    ADS  Google Scholar 

  71. B.A. Berg: Int. J. Mod. Phys. C 3, 1083 (1992)

    ADS  Google Scholar 

  72. B. Dünweg: In Monte Carlo and Molecular Dynamics of Condensed Matter Systems, ed. by K. Binder, G. Ciccotti (Società Italiana di Fisica, Bologna 1996) p. 215

    Google Scholar 

  73. D. Frenkel, B. Smit: Understanding Molecular Simulation: From Algorithms to Applications (Academic, San Diego 1996)

    MATH  Google Scholar 

  74. C.H. Bennett: J. Comput. Phys. 22, 245 (1976)

    ADS  Google Scholar 

  75. J.P. Valleau, D.N. Card: J. Chem. Phys. 57, 5457 (1972)

    ADS  Google Scholar 

  76. G.M. Torrie, J.P. Valleau: J. Comp. Phys. 23, 187 (1977); Chem. Phys. Lett. 28, 578 (1974)

    ADS  Google Scholar 

  77. J.P. Valleau, G.M. Torrie: In Statistical Mechanics, Part A: Equilibrium Techniques, ed. by B.J. Berne (Plenum, New York 1977)

    Google Scholar 

  78. B.A. Berg, T. Neuhaus: Phys. Rev. Lett. 68, 9 (1992)

    ADS  Google Scholar 

  79. U. Hansmann, B.A. Berg, T. Neuhaus: Int’l J. Mod. Phys. C 3, 1155 (1992)

    ADS  Google Scholar 

  80. B.A. Berg, U. Hansmann, T. Neuhaus: Phys. Rev. B 47, 497 (1993)

    ADS  Google Scholar 

  81. B.A. Berg, U. Hansmann, T. Neuhaus: Z. Physik B 90, 229 (1993)

    ADS  Google Scholar 

  82. E. Marinari, G. Parisi: Europhys. Lett. 19, 457 (1992)

    ADS  Google Scholar 

  83. A.P. Lyubartsev, A.A. Martsinovski, S.V. Sherkenov, P.N. Vorontsov-Velyaminov: J. Chem. Phys. 96, 1776 (1992)

    ADS  Google Scholar 

  84. P.M.C. de Oliveira, T.S.P. Penna, H.J. Herrmann: Brazilian J. Phys. 26, 677 (1996)

    ADS  Google Scholar 

  85. J. Lee: Phys. Rev. Lett. 71, 211 (1993)

    ADS  Google Scholar 

  86. N.A. Alves, B.A. Berg, R. Villanova: Phys. Rev. B 41, 383 (1990)

    ADS  Google Scholar 

  87. G. Bhanot, S. Black, P. Carter, R. Salvador: Phys. Lett. B 183, 331 (1987);

    ADS  Google Scholar 

  88. G. Bhanot, R. Salvador, S. Black, R. Toral: Phys. Rev. Lett. 59, 803 (1987)

    ADS  Google Scholar 

  89. W. Janke, S. Kappler: Phys. Rev. Lett. 74, 212 (1995)

    ADS  Google Scholar 

  90. N.B. Wilding, A.D. Bruce: J. Phys: Condens. Matter 4, 3087 (1992)

    ADS  Google Scholar 

  91. N.B. Wilding: Z. Physik B 93, 113 (1993)

    ADS  Google Scholar 

  92. N.B. Wilding, M. Müller: J. Chem. Phys. 102, 2562 (1995)

    ADS  Google Scholar 

  93. N.B. Wilding: Phys. Rev. E 52, 602 (1995)

    ADS  Google Scholar 

  94. M. Müller, N.B. Wilding: Phys. Rev. E 51, 2079 (1995)

    ADS  Google Scholar 

  95. N.B. Wilding, M. Müller, K. Binder: J. Chem. Phys. 105, 802 (1996)

    ADS  Google Scholar 

  96. N.B. Wilding, K. Binder: Physica A 231, 439 (1996)

    ADS  Google Scholar 

  97. N.B. Wilding, P. Nielaba: Phys. Rev. E 53, 926 (1996)

    ADS  Google Scholar 

  98. N.B. Wilding: Annual Reviews of Computational Physics IV, ed. by D. Stauffer (World Scientific, Singapore 1996) p. 37

    Google Scholar 

  99. N.B. Wilding: In Computer Simulation Studies in Condensed Mattter VIII, ed. by D.P. Landau, K.K. Mon, H.B. Schüttler, Springer Proc. Phys. 80, 18 (Springer, Berlin, Heidelberg 1995)

    Google Scholar 

  100. E. Riedel, F.J. Wegner: Z. Physik 225, 195 (1969)

    ADS  Google Scholar 

  101. M.E. Fisher: Rev. Mod. Phys. 46, 597 (1994)

    ADS  Google Scholar 

  102. K. Binder, H.P. Deutsch: Europhys. Lett. 18, 667 (1992)

    ADS  Google Scholar 

  103. H.P. Deutsch, K. Binder: J. Phys. II (France) 3, 1049 (1993)

    Google Scholar 

  104. K.K. Mon, K. Binder: Phys. Rev. E 48, 2498 (1993)

    ADS  Google Scholar 

  105. E. Luijten, H.W.J. Blöte, K. Binder: Phys. Rev. E 54, 4626 (1996)

    ADS  Google Scholar 

  106. K. Binder, R. Evans, D.P. Landau, A.M. Ferrenberg: Phys. Rev. E 53, 5023 (1996)

    ADS  Google Scholar 

  107. A. Coniglio, W. Klein: J. Phys. A 13, 2775 (1980)

    ADS  Google Scholar 

  108. C.K. Hu: Phys. Rev. B 29, 5103 (1984)

    ADS  Google Scholar 

  109. M.E. Fisher: Physics 3, 267 (1967)

    Google Scholar 

  110. K. Binder: Ann. Phys. 98, 390 (1976)

    ADS  Google Scholar 

  111. K. Binder, J.-S. Wang: J. Stat. Phys. 55, 87 (1989)

    MathSciNet  ADS  Google Scholar 

  112. J.L. Cardy: In Phase Transitions and Critical Phenomena 11, 55 (Academic, New York 1987)

    Google Scholar 

  113. D.P. Landau, S. Tang, S. Wansleben: J. Phys. (Paris) Coll. C8, 49, 1525 (1988)

    Google Scholar 

  114. A.M. Ferrenberg, D.P. Landau, Y.J. Wong: Phys. Rev. Lett. 69, 3382 (1992)

    ADS  Google Scholar 

  115. K. Binder: In Monte Carlo and Molecular Dynamics Simulations in Polymer Science, ed. by K. Binder (Oxford Univ. Press, New York 1995) p. 356

    Google Scholar 

  116. H.-P. Deutsch: J. Stat. Phys. 67, 1039 (1992)

    ADS  MATH  Google Scholar 

  117. H.-P. Deutsch, K. Binder: Macromolecules 25, 6214 (1992)

    ADS  Google Scholar 

  118. A. Sariban, K. Binder: J. Chem. Phys. 86, 5859 (1987)

    ADS  Google Scholar 

  119. I. Carmesin, K. Kremer: Macromol. 21, 2819 (1988);

    ADS  Google Scholar 

  120. H.-P. Deutsch, K. Binder: J. Chem. Phys. 94, 2294 (1991)

    ADS  Google Scholar 

  121. K. Binder: In Festkörperprobleme (Advances in Solid State Physics) 26, 133 (Vieweg, Braunschweig 1986)

    Google Scholar 

  122. H.-P. Deutsch, K. Binder: Macromol. Chem., Macromol. Symp. 65, 59 (1993)

    Google Scholar 

  123. H.-P. Deutsch: J. Chem. Phys. 99, 4825 (1993)

    ADS  Google Scholar 

  124. M. Müller, K. Binder: Macromolecules 28, 1825 (1995)

    ADS  Google Scholar 

  125. J.J. Rehr, N.D. Mermin: Phys. Rev. A 8, 472 (1973)

    ADS  Google Scholar 

  126. A.Z. Panagiotopolous: Molec. Phys. 61, 813 (1987); Molecular Simulation 9, 1 (1992)

    ADS  Google Scholar 

  127. A.Z. Panagiotopolous: In Supercritical Fluids-Fundamentais for Application ed. by E. Kiran, J.M.H. Levelt-Sengers (Kluwer, Dordrecht 1994)

    Google Scholar 

  128. D. Frenkel, B. Smit: Understanding Molecular Simulation: From Algorithms to Applications (Academic, San Diego 1996)

    MATH  Google Scholar 

  129. M.P. Allen: In Monte Carlo and Molecular Dynamics of Condensed Matter Systems, ed. by K. Binder, G. Ciccotti (Società Italiana di Fisica, Bologna 1996) p. 255

    Google Scholar 

  130. K. Binder, D.P. Landau: Phys. Rev. B 13, 1140 (1976)

    ADS  Google Scholar 

  131. R.B. Stinchcombe: In Phase Transitions and Critical Phenomena, 7, 151 (Academic, London 1983)

    Google Scholar 

  132. T. Nattermann, J. Villain: Phase Transitions 11, 5 (1988)

    Google Scholar 

  133. W. Selke, L.N. Shchur, A.L. lalapov: In Animai Reviews of Computational Physics 1, 17 (World Scientific, Singapore 1994)

    Google Scholar 

  134. H. Rieger: Phys. Rev. B 52, 6659 (1995)

    ADS  Google Scholar 

  135. M. D’Onorio de Meo, J.D. Reger, K. Binder: Physica A 220, 628 (1995)

    ADS  Google Scholar 

  136. V. Pereyra, P. Nielaba, K. Binder: Z. Physik B 97, 197 (1995)

    Google Scholar 

  137. K. Eichhorn, K. Binder; Europhys. Lett. 30, 331 (1995); J. Phys: Condensed Matter 8, 5209 (1996)

    ADS  Google Scholar 

  138. I.D. Lawrie, S. Sarbach: In Phase Transitions and Critical Phenomena 9, 1 (Academic, London 1984)

    Google Scholar 

  139. V.L. Ginzburg: Sov. Phys. Solid State 2, 1824 (1960)

    MathSciNet  Google Scholar 

  140. P.G. de Gennes: J. Phys. (Paris) Lett. 38, L-441 (1977);

    Google Scholar 

  141. J.F. Joanny: J. Phys. A 11, L-117 (1978);

    ADS  Google Scholar 

  142. K. Binder: J. Chem. Phys. 79, 6387 (1983)

    ADS  Google Scholar 

  143. G. Kamieniarz, H.W.J. Blöte: J. Phys. A 26, 201 (1993)

    ADS  Google Scholar 

  144. E. Brézin, J. Zinn-Justin: Nucl. Phys. B 257, 867 (1985)

    ADS  Google Scholar 

  145. M.B. Bouabci, C.E.I. Carneiro: Phys. Rev. 1354, 359 (1996)

    Google Scholar 

  146. M. Blume, V.J. Emery, R.B. Griffiths: Phys. Rev. A 4, 4946 (1976)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Physik, Johannes Gutenberg Universität, Staudingerweg 7, D-55099, Mainz, Germany

    Professor Dr. Kurt Binder

  2. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69020, Heidelberg, Germany

    Professor Dr. Dieter W. Heermann

Authors
  1. Professor Dr. Kurt Binder
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Professor Dr. Dieter W. Heermann
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Binder, K., Heermann, D.W. (1997). Some Important Recent Developments of the Monte Carlo Methodology. In: Monte Carlo Simulation in Statistical Physics. Springer Series in Solid-State Sciences, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03336-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-03336-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63265-8

  • Online ISBN: 978-3-662-03336-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation