An Investigation Into Growing Correlation Lengths in Glassy Systems

  • Christopher Fullerton

Student thesis: Phd


In this thesis Moore and Yeo's proposed mapping of the structural glass to the Ising spin glass in a random field is presented. In contrast to Random First Order Theory and Mode Coupling Theory, this mapping predicts that there should be no glass transition at finite temperature. However, a growing correlation length is predicted from the size of rearranging regions in the supercooled liquid, and from this a growing structural relaxation time is predicted. Also presented is a study of the propensity of binary fluids (i.e. fluids containing particles of two sizes) to phase separate into regions dominated by one type of particle only. Binary fluids like this are commonly used as model glass formers and the study shows that this phase separation behaviour is something that must be taken into account.The mapping relies on the use of replica theory and is therefore very opaque. Here a model is presented that may be mapped directly to a system of spins, and also prevents the process of phase separation from occurring in binary fluids. The system of spins produced in the mapping is then analysed through the use of an effective Hamiltonian, which is in the universality class of the Ising spin glass in a random field. The behaviour of the correlation length depends on the spin-spin coupling J and the strength of the random field h. The variation of these with packing fraction φ and temperature T is studied for a simple model, and the results extended to the full system. Finally a prediction is made for the critical exponents governing the correlation length and structural relaxation time.
Date of Award1 Aug 2012
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorMichael Moore (Supervisor)


  • Effective Hamiltonian
  • Statistical Mechanics
  • Spin Glass
  • Molecular Dynamics
  • Disordered Systems
  • Glassy Systems
  • Glass
  • Soft Matter

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