Skip to main content
SpringerLink
Log in

From Varenna (1970) to Como (1995): Kurt Binder’s long walk in the land of criticality

  • Published:
The European Physical Journal H Aims and scope Submit manuscript

Abstract

This paper aims at contributing to the history of early computational statistical mechanics. The topic concerns the physics near a critical point and how long it took for Monte Carlo (MC) simulations to be seriously considered by the community as a valid and important tool to analyze critical phenomena. We will focus on one of the leading scientific figures behind this effort: Kurt Binder, whose scientific achievements were acknowledged by the award of the Boltzmann medal in 2007. Kurt Binder, who is now 75, has retired, some years ago, from a Professorship at the University of Mainz.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alder, B.J. and T.E. Wainwright. 1957. Phase Transition for a Hard Sphere System. J. Chem. Phys. 27:1208–1209.

    Article  ADS  Google Scholar 

  2. Alder, B.J. and T.E. Wainwright. 1958, Molecular Dynamics by Electronic Computers, in International Symposium on the Statistical Mechanical Theory of Transport Processes, Brussels, 1956, edited by I. Prigogine (Interscience, New York), pp. 97–131.

  3. Baumgärtner, A. and K. Binder. 1979. Dynamics of the Helix-Coil Transition in Biopolymers. J. Chem. Phys. 70:429–437.

    Article  ADS  Google Scholar 

  4. Bernard, E.P. and W. Krauth. 2011. Two-steps melting in two dimensions: First-order Liquid-Hexatic Transition. Phys. Rev. Lett. 107:155704.

    Article  ADS  Google Scholar 

  5. Binder, K. and H. Rauch. 1967a. Berechnung der Richtungsverteilung von Neutronen hinter einem gekrümmten totalreflektierenden Kollimatorschlitz? ATKE 12:145–158.

    Google Scholar 

  6. Binder, K. and H. Rauch. 1967b. Berechnung der spektralen Verteilung von Neutronen hinter einem gekrümmten totalreflektierenden Kollimatorschlitz? ATKE 12:337–342.

    Google Scholar 

  7. Binder, K. and H. Rauch. 1968. Calculation of spin-correlation functions in a ferro-magnet with a Monte Carlo method. Phys. Lett. A 27:247–248.

    Article  ADS  Google Scholar 

  8. Binder, K. and H. Rauch, H. 1969. Numerische Berechnung von Spin-Korrelationsfunktionen und Magnetisierungskurven von Ferromagnetika. Z. Phys. 219:201–215.

    Article  ADS  Google Scholar 

  9. Binder, K. 1972a. Statistical Mechanics of Finite Three-dimensional Ising Models. Physica 62:508–526.

    Article  ADS  Google Scholar 

  10. Binder, K. and D. Stauffer. 1972b. Monte Carlo Study of the Surface Area of Liquid Droplets. J. Stat. Phys. 6:49–59.

    Article  ADS  Google Scholar 

  11. Binder, K. and P.C. Hohenberg. 1972c. Phase Transitions and Static Spin Correlation Functions in Ising Models with Free Surfaces. Phys. Rev. B 6:3461–3487.

    Article  ADS  Google Scholar 

  12. Binder, K. 1973. Time-Dependent Ginzburg-Landau Theory of Non-equilibrium Relaxation. Phys. Rev. B 8:3423–3438.

    Article  ADS  Google Scholar 

  13. Binder, K. 1974. Monte Carlo Computer Experiments on Critical Phenomena and Metastable States. Adv. Phys. 23:917–939.

    Article  ADS  Google Scholar 

  14. Binder, K. and K. Schröder. 1976. Phase Transitions of a Nearest-Neighbor Ising “Spin Glass”. Phys. Rev. B 14:2142–2152.

    Article  ADS  Google Scholar 

  15. Binder, K. 1981. Finite Size analysis of Ising model Block Distribution Functions. Zeit. Phys. B: Condens. Matter 43:119–140.

    Article  ADS  Google Scholar 

  16. Binder, K. and A.P. Young. 1986. Spin Glasses: Experimental Facts, Theoretical Concepts and Open Questions. Rev. Mod. Phys. 58:810–976.

    Article  ADS  Google Scholar 

  17. Binder, K. and G. Ciccotti. 1996. Monte Carlo and Molecular Dynamics of Condensed Matter Systems. Societa Italiana di Fisica, Bologna. ISBN 88-7794-078-6.

  18. Callen, H.B. and T.A. Welton. 1951. Irreversibility and Generalized Noise. Phys. Rev. 83:34–40.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Cardy, J.L. 1988. Finite-size Scaling, in Current Physics, Sources and Comments, edited by H. Rubinstein, North-Holland, Amsterdam, Vol. 2.

  20. Chandler, D. 1987. Introduction to Modern Statistical Mechanics, Oxford University Press, New York.

  21. Das S.K., M.E. Fisher, J.V. Sengers, J. Horbach and K. Binder. 2008. Critical Dynamics in a Binary Fluid: Simulations and Finite-Size Scaling. Phys. Rev. Lett. 97:025702.

    Article  ADS  Google Scholar 

  22. Domb, C. 1996. The Critical Point: A Historical Introduction to the Modern Theory of Critical Phenomena. Taylor and Francis, Bristol.

  23. Dünweg, B. 1996. Simulation of Phase Transitions: Critical Phenomena, in [Binder 1996].

  24. Erhman, J.P., L.D. Fosdick and D.C. Handscomb. 1960. Computation of the Order Parameter in an Ising Lattice by the Monte Carlo Method. J. Math. Phys. 1:547–558.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Ferrenberg, A.M., J. Xu and D.P. Landau. 2018. Pushing the Limits of Monte Carlo Simulations for the Three-dimensional Ising Model. Phys. Rev. E 97:043301.

    Article  ADS  Google Scholar 

  26. Fisher, M.E. 1967. The theory of Equilibrium Critical Phenomena. Rep. Prog. Phys. 30:615.

    Article  ADS  Google Scholar 

  27. Fisher, M.E. 1971. Lecture notes in the proceedings of the Varenna summer school [Green 1971].

  28. Fisher, M.E. and M.N. Barber. 1972. Scaling Theory for Finite-Size Effects in the Critical Region. Phys. Rev. Lett. 28:1516–1519.

    Article  ADS  Google Scholar 

  29. Fisher, M.E. 1983. Scaling, Universality and Renormalization Group Theory. In Critical Phenomena, Lecture Notes in Physics, edited by F.W.J. Hahne, Springer (Berlin), Vol. 186, pp. 1–139.

    Article  ADS  Google Scholar 

  30. Friedberg, R. and J.E. Cameron. 1970. Test of the Monte Carlo Method: Fast Simulation of a Small Ising Lattice. J. Chem. Phys. 52:6049–6058.

    Article  ADS  Google Scholar 

  31. Green, M.S. 1951. Brownian Motion in a Gas of Non-interacting Particles. J. Chem. Phys. 19:1036–1046.

    Article  ADS  MathSciNet  Google Scholar 

  32. Green, M.S. 1971. Proceedings of the International School of Physics “Enrico Fermi” on Critical Phenomena. Course No 51, edited by M.S. Green, Academic Press, New York.

  33. Heller, P. 1967. Experimental Investigations of Critical Phenomena. Rep. Prog. Phys. 30:731.

    Article  ADS  Google Scholar 

  34. Kadanoff, L.P. et al. 1967. Static Phenomena near Critical Points: Theory and Experiments. Rev. Mod. Phys. 39:395–431.

    Article  ADS  Google Scholar 

  35. Kadanoff, L.P. 1986. On two levels. Phys. Today 39:7–8.

    Google Scholar 

  36. Kaganov, M.I. and A.N. Omel’yanchuk. 1971. Zh. Eksp. i. Teor. Fiz 61:1691; see also M.I. Kaganov and A.N. Omel’yanchuk, Sov. Phys. JETP 34:895 (1972).

    Google Scholar 

  37. Kremer, K., A. Baumgärtner and K. Binder. 1981. Monte Carlo Renormalization of Hard Sphere Polymer Chains in Two to Five Dimensions. Z. Phys. B 40:331–341.

    Article  ADS  Google Scholar 

  38. Kubo, R. 1957. Statistical Mechanical Theory of Irreversible Processes (I). J. Phys. Soc. Jpn. 12:570–586.

    Article  ADS  Google Scholar 

  39. Landau, D.P. 1976. Finite-size Behavior of the Ising Square Lattice. Phys. Rev. B 13:2997–3011.

    Article  ADS  Google Scholar 

  40. Landau, D.P. and K. Binder. 2005. Monte Carlo Simulations in Statistical Physics, Cambridge University Press, Cambridge, second edition.

  41. Levesque, D. and J.-P. Hansen. 2018. The origin of computational Statistical Mechanics in France. Eur. Phys. J. H 44:37–46.

    Article  Google Scholar 

  42. Mareschal, M. 2018. Early Years of Computational Statistical Mechanics. Eur. Phys. J. H 43:293–302.

    Article  Google Scholar 

  43. Mareschal, M. and B.L. Holian. 1992. Molecular Simulations of Complex Hydrodynamic Phenomena, Plenum Press, New York.

  44. Mauro, F., G. Ciccotti and K. Binder (Editors). 2006. Computer Simulations in Condensed Matter: From Materials to Chemical Biology, vols. 1 and 2. Lect. Notes Phys. 703, Springer, Berlin, Heidelberg.

  45. Metropolis, N. and S. Ulam. 1949, The Monte Carlo Method. J. Am. Stat. Assoc. 44:335–341.

    Article  MATH  Google Scholar 

  46. Metropolis, N., A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller. 1953. Equations of State Calculations by Fast Computing Machines. J. Chem. Phys. 21:1087–1092.

    Article  ADS  Google Scholar 

  47. Müller-Krumbhaar, H. and K. Binder. 1973. Dynamic Properties of the Monte Carlo Method in Statistical Mechanics. J. Stat. Phys. 8:1–24.

    Article  ADS  Google Scholar 

  48. Nightingale, M.P. 1976. Scaling Theory and Finite Systems. Physica 83A:561–572.

  49. Niss, M. 2005. History of the Lenz-Ising Model 1920-1950: From ferromagnetic to cooperative phenomena. Arch. Hist. Exact Sci. (2005) 59:267–318.

    Article  MathSciNet  MATH  Google Scholar 

  50. Niss, M. 2009. History of the Lenz-Ising Model 1950-1965: from irrelevance to relevance. Arch. Hist. Exact Sci. 63:243–287.

    Article  MathSciNet  MATH  Google Scholar 

  51. Niss, M. 2011. History of the Lenz-Ising Model 1965–1971: the role of a simple model in understanding critical phenomena. Arch. Hist. Exact Sci. 65:625–658.

    Article  MathSciNet  MATH  Google Scholar 

  52. Onsager, L. 1944. Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition. Phys. Rev. 65:117–149.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. Orkoulas, G., A.Z. Panagiotopoulos and M.E. Fisher. 2000. Criticality and crossover in accessible regimes. Phys. Rev. E 61:5930–5939.

    Article  ADS  Google Scholar 

  54. Plischke M. and B. Bergersen. 2006. Equilibrium Statistical Mechanics, 3rd edn, World Scientific, Singapore.

  55. Rahman, A. 1964. Correlations in the Motion of Atoms in Liquid Argon. Phys. Rev. A 136:405–411.

    Article  ADS  Google Scholar 

  56. Rosenbluth, M.N. and A.W. Rosenbluth. 1954. Monte Carlo Calculation of the Average Extension of Molecular Chains. J. Chem. Phys. 23:356–359.

    Article  ADS  Google Scholar 

  57. Stanley, H.E. 1971. Introduction to Phase Transitions and Critical Phenomena. Clarendon Press, Oxford.

  58. Stoll, E., K. Binder and T. Schneider. 1972. Evidence for Fisher’s Droplet Model in Simulated Two-Dimensional Cluster Distributions. Phys. Rev. B 6:2777–2780.

    Article  ADS  Google Scholar 

  59. Swendsen, R.H. and J.-S. Wang. 1987. Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 58:86–88.

    Article  ADS  Google Scholar 

  60. Torrie, G.M. and J.P. Valleau. 1977. Non-physical Sampling Distributions in Monte Carlo Free-energy Estimation: Umbrella Sampling. J. Comput. Phys. 23:187–199.

    Article  ADS  Google Scholar 

  61. Van Hove, L. 1954. Time-dependent Correlations between Spins and Neutron Scattering in Ferromagnetic Crystals. Phys. Rev. 95:1374–1384.

    Article  ADS  MATH  Google Scholar 

  62. Verlet, L. 1967. Computer Experiments on Classical Fluids. (I). Phys. Rev. 159:98–103.

    Article  ADS  Google Scholar 

  63. Widom, B. 1975. Critical Phenomena, in Fundamental Problems in Statistical Mechanics III, E.G.D. Cohen Editor, North-.

  64. Wilson, K.G. 1971a. Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture. Phys. Rev. B 4:3174–3184.

    Article  ADS  MATH  Google Scholar 

  65. Wilson, K.G. 1971b. Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior. Phys. Rev. B 4:3184–3205.

    Article  ADS  MATH  Google Scholar 

  66. Wood, W.W. and J.D. Jacobson. 1957. Preliminary Results from the Recalculation of the Equation of State of Hard Spheres. J. Chem. Phys. 27:1207–1208.

    Article  ADS  Google Scholar 

  67. Xu, J., S.-H. Tsai, D.P. Landau and K. Binder. 2019. Finite-size scaling for a first-order transition where a continuous symetry is broken: the spin-flop transition in the three-dimensional XXZ Heisenberg antiferromagnet. Phys. Rev. E 99:023309.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departement de Physique, CP 223, Université Libre de Bruxelles, Bruxelles, Belgium

    Michel Mareschal

Authors
  1. Michel Mareschal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michel Mareschal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mareschal, M. From Varenna (1970) to Como (1995): Kurt Binder’s long walk in the land of criticality. EPJ H 44, 161–179 (2019). https://doi.org/10.1140/epjh/e2019-100016-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjh/e2019-100016-3

Search

Navigation