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Theory of glass transition in spin glasses, orientational glasses and structural glasses

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25 Years of Non-Equilibrium Statistical Mechanics

Part of the book series: Lecture Notes in Physics ((LNP,volume 445))

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Abstract

Theoretical concepts about the glass transition are briefly reviewed, and the test of these ideas by Monte Carlo simulations of simple lattice models is described, with an emphasis on isotropic and anisotropic orientational glasses, and the bond fluctuation model of polymer melts. It is suggested that orientational glasses do have an equilibrium phase transition at zero temperature (in d = 3 dimensions!) only, in contrast to the Ising spin glass which orders at nonzero temperature. A diverging glass correlation length is identified that is responsible for the anomalous slowing down. For the Potts glass, the divergence seems to be exponential, implying that the model is at its lower critical dimensionality.

Choosing a Hamiltonian that prefers a long bond of the bond fluctuation model of polymer chains, the resulting “geometric frustration” in systems of densely packed chains leads to a glassy freeze-in, surprisingly similar to experiment. Expectations of various theories are qualitatively verified. It is suggested that also in this model a diverging length can be identified.

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Authors and Affiliations

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

    K. Binder

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  1. K. Binder
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J. J. Brey J. Marro J. M. Rubí M. San Miguel

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© 1995 Springer-Verglag

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Binder, K. (1995). Theory of glass transition in spin glasses, orientational glasses and structural glasses. In: Brey, J.J., Marro, J., Rubí, J.M., San Miguel, M. (eds) 25 Years of Non-Equilibrium Statistical Mechanics. Lecture Notes in Physics, vol 445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59158-3_40

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  • DOI: https://doi.org/10.1007/3-540-59158-3_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59158-0

  • Online ISBN: 978-3-540-49203-0

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