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Theoretical and Mathematical Physics

, Volume 141, Issue 1, pp 1443–1451 | Cite as

A Simple Cluster Model for the Liquid–Glass Transition

  • V. N. Ryzhov
  • E. E. Tareyeva
  • T. I. Schelkacheva
  • N. M. Chtchelkatchev
Article

Abstract

Using the classical distribution-function approach to simple liquids, we estimate the orientational interaction between clusters consisting of a particle and its nearest neighbors. We show that there are density and temperature ranges where the interaction changes sign as a function of the cluster radius. On this basis, the corresponding model of interacting cubic and icosahedral clusters (of the type of a spin glass model) is proposed and solved in the replica-symmetric approximation. We show that the glass order parameter grows continuously on cooling and the replica-symmetry-breaking temperature can be identified with the glass transition temperature. We also show that on cooling a system of particles with a Lennard-Jones interaction, cubic clusters freeze first. The transition temperature for icosahedral clusters is somewhat lower; therefore, the cubic structure of the short-range order is more likely in a Lennard-Jones glass near transition.

short-range order local structure of liquid orientational glass 

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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • V. N. Ryzhov
    • 1
  • E. E. Tareyeva
    • 1
  • T. I. Schelkacheva
    • 1
  • N. M. Chtchelkatchev
    • 1
    • 2
  1. 1.Institute for High-Pressure PhysicsMoscow OblastRussia
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

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