Abstract
We have seen how, in the first thirty years following its birth and with the first encouraging results obtained through the study of simple model systems, molecular simulation had grown in all possible directions, imposing the effectiveness of its own methods for a complete realization of the programme of statistical mechanics: derivation and explicit calculation, starting from the basic building blocks (i.e., atoms) and from the fundamental laws of physics, of the properties of the aggregate states of matter in its various forms, and of the transitions between them.
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Notes
- 1.
W.L. McMillan , Ground State of Liquid He4, Physical Review A 138, 442, 1965.
- 2.
M.H. Kalos , Monte Carlo Calculations of the Ground State of Three- and Four-Body Nuclei, Physical Review 128, 1791, 1962.
- 3.
M.H. Kalos , D. Levesque , L. Verlet , Helium at zero temperature with hard-sphere and other forces, Physical Review A 9, 2178, 1974.
- 4.
D.M. Ceperley , Ground state of the fermion one-component plasma: A Monte Carlo study in two and three dimensions, Physical Review B 18, 3126, 1978.
- 5.
D.M. Ceperley , M.H. Kalos , Quantum many-body problems, in Monte Carlo Methods in Statistical Physics, ed. by K. Binder , Springer-Verlag 1979.
- 6.
This quote by Alder , and the following, can be found in D. Mac Kernan et al., Interview with Berni Alder , SIMU Newsletter n.4, 2002, https://doi.org/10.13140/2.1.2562.7843, https://www.researchgate.net/publication/267979976_SIMU_Challenges_in_Molecular_Simulations_Bridging_the_Length_and_Timescales_gap_Volume_4.
- 7.
D.M. Ceperley , B.J. Alder, Ground state of electron gas by a stochastic method, Physical Review Letters 45, 776, 1980.
- 8.
This quote by Ceperley , and the following, unless otherwise stated, come from D. Ceperley , A Quantum History, personal communication to the authors, June 18, 2018.
- 9.
D.M. Ceperley , B.J. Alder , The calculation of the properties of metallic hydrogen using Monte Carlo, Physica B 108, 875, 1981; D.M. Ceperley , B.J. Alder, Ground state of solid hydrogen at high pressure, Physical Review B 36, 2092, 1987.
- 10.
R.P. Feynman , The λ-Transition in Liquid Helium, Physical Review 90, 1116, 1953; R.P. Feynman , Atomic Theory of the λ Transition in Helium, Physical Review 91, 1291, 1953; R.P. Feynman , Atomic Theory of Liquid Helium, Physical Review 91, 1301, 1953.
- 11.
D. Chandler , P.G. Wolynes, Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids, Journal of Chemical Physics 74, 4078, 1981.
- 12.
J. Barker , A quantum-statistical Monte Carlo method; path integrals with boundary conditions, Journal of Chemical Physics 70, 2914, 1979.
- 13.
R.P. Feynman , Simulating physics with computers, International Journal of Theoretical Physics 21, 467, 1982.
- 14.
B.J. Alder , D.M. Ceperley , E.L. Pollock, Computer simulation of phase transitions in classical and quantum systems, in Proceedings of the International Symposium on Quantum Chemistry, Theory of Condensed Matter, and Propagator Methods in the Quantum Theory of Matter, International Journal of Quantum Chemistry 22 (S16), 49, 1982; E.L. Pollock, D.M. Ceperley , Simulation of quantum many-body systems by path integral methods, Physical Review B 30, 2555, 1984; D.M. Ceperley , E.L. Pollock, Path-integral computation of the low-temperature properties of liquid 4He, Physical Review Letters 56, 351, 1986.
- 15.
D.M. Ceperley , Path integrals in the theory of condensed helium, Review of Modern Physics 67, 279, 1995.
- 16.
D.M. Ceperley , G. Jacucci , Calculation of exchange frequencies in bcc 3He with the path integral Monte Carlo method, Physical Review Letters 58, 1648, 1987.
- 17.
D. Ceperley , Fermion nodes, Journal of Statistical Physics 63, 1237, 1991; D. Ceperley , Path-integral calculations of normal liquid 3He, Physical Review Letters 69, 331, 1992.
- 18.
L. Onsager , Crystal statistics. I. A two-dimensional model with an order-disorder transition, Physical Review 65, 117, 1944.
- 19.
This quote and the following come from the interview given by Binder on October 2, 2018 at the University of Mainz, never published, and sent to the authors by the interviewer, M. Mareschal .
- 20.
L. Kadanoff et al., Static phenomena near critical points: Theory and experiments, Review of Modern Physics 39, 395, 1967; M.E. Fisher , The theory of equilibrium critical phenomena, Reports on Progress in Physics 30, 615, 1967.
- 21.
K. Binder , H. Rauch , Calculation of spin-correlation functions in a ferromagnet with a Monte Carlo method, Physics Letters A 27, 247, 1968.
- 22.
H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Clarendon Press, Oxford, 1971.
- 23.
K. Binder , From the Lake of Como to surface critical phenomena, in J. Brujic, A Grosberg (eds.), Memories of Pierre Hohenberg , New York 2018, pp. 30–34, cit. p. 31. Wilson’s papers on the renormalization group are: K.G. Wilson , Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture, Physical Review B 4, 3174, 1971; K.G. Wilson , Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior, Physical Review B 4, 3184, 1971.
- 24.
K. Binder , P.C. Hohenberg , Phase transitions and static spin correlations in Ising models with free surfaces, Physical Review B 6, 3461, 1972.
- 25.
K. Binder , H. Müller-Krumbhaar , Monte Carlo calculation of the scaling equation of state for the classical Heisenberg ferromagnet, Physical Review B 7, 3297, 1973.
- 26.
H. Müller-Krumbhaar , K. Binder , Dynamic properties of the Monte Carlo method in statistical mechanics, Journal of Statistical Physics 8, 1, 1973.
- 27.
K. Binder , D. Stauffer , Monte Carlo study of the surface area of liquid droplets, Journal of Statistical Physics 6, 49, 1972; K. Binder , D. Stauffer , H. Müller-Krumbhaar , Calculation of dynamic critical properties from a cluster reaction theory, Physical Review B 10, 3853, 1974; K. Binder , D. Stauffer , Statistical theory of nucleation, condensation and coagulation, Advances of Physics 25, 343, 1976.
- 28.
K. Binder , P.C. Hohenberg , Surface effects on magnetic phase transitions, Physical Review B 9, 2194, 1974.
- 29.
K. Binder , M.H. Kalos , J.L. Lebowitz , J. Marro, Computer experiments on phase separation in binary alloys, Advances in Colloid and Interface 10, 173, 1979.
- 30.
K. Binder , K. Schröder, Monte Carlo study of a two-dimensional Ising “spin glass”, Solid State Communications 18, 1361, 1976; K. Binder , K. Schröder, Phase transitions of a nearest-neighbor Ising “spin glass”, Physical Review B 14, 2142, 1976.
- 31.
K. Binder , D.P. Landau , Critical properties of the two-dimensional anisotropic Heisenberg model, Physical Review B 13, 1140, 1976.
- 32.
K. Binder , Monte Carlo study of thin magnetic Ising films, Thin Solid Films 20, 367, 1974.
- 33.
K. Binder , Finite size analysis of Ising model block distribution functions, Zeitschrift für Physik B 43, 119, 1981.
- 34.
K. Binder (ed.), Monte Carlo Methods in Statistical Physics, Springer-Verlag 1979.
- 35.
His main motivation was to explain experimentally, in collaboration with David Landau , observed phenomena in various branches of solid state or surface physics. Another study, jointly with Joel Lebowitz and Mal Kalos , addressed long- and short-range order in alloys.
- 36.
A. Baumgärtner , K. Binder , Monte Carlo studies on the freely jointed polymer chain with excluded volume interaction, Journal of Chemical Physics 71, 2541, 1979. The history of the joint development of theory and simulation of polymers has still to be written. However, it is worth noting that the theoretical physics of polymers was founded in the 1940s by Paul Flory , who later won the Nobel Prize for Chemistry for his work. The phase diagrams of polymer solutions and polymer blends were then modelled by what is now known as “Flory -Huggins theory”, which became a kind of “gold standard” for experimentalists: P.J. Flory, Thermodynamics of high polymer solutions, Journal of Chemical Physics 9, 660, 1941; M.L. Huggins, Solutions of long chain compounds, Journal of Chemical Physics 9, 440, 1941. Only in 1987 were the deficiencies of this mean-field theory shown by a Monte Carlo simulation: A. Sariban, K. Binder , Critical properties of the Flory -Huggins lattice model of polymer mixtures, Journal of Chemical Physics 86, 5859, 1987.
- 37.
Kurt Binder interview by D. Mac Kernan, SIMU Newsletter 3, 19, 2001.
- 38.
M. Mareschal , From Varenna (1971) to Como (1995): Kurt Binder’s long walk in the land of criticality, European Physics Journal H 44, 161, 2019. It is worth noting that the attempts by simulators to study models of polymers by the numerical approach began with Metropolis MC (1953). Only two years later, the two Rosenbluths published their famous algorithm which opened the way to the study of restricted random walks on a lattice: M.N. Rosenbluth, A.W. Rosenbluth, Monte Carlo calculation of the average extension of molecular chains, Journal of Chemical Physics 23, 356, 1955. Many researchers have since taken up the challenge of extending the Rosenbluth algorithm.
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Battimelli, G., Ciccotti, G., Greco, P. (2020). Quantum Systems and Critical Phenomena. In: Computer Meets Theoretical Physics. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-030-39399-1_7
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