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An Investigation Into Growing Correlation Lengths in Glassy Systems

Fullerton, Christopher James

[Thesis]. Manchester, UK: The University of Manchester; 2011.

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Abstract

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.

Bibliographic metadata

Type of resource:
Content type:
Form of thesis:
Type of submission:
Degree type:
Doctor of Philosophy
Degree programme:
PhD Physics
Publication date:
Location:
Manchester, UK
Total pages:
179
Abstract:
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.
Thesis main supervisor(s):
Thesis advisor(s):
Language:
en

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:140566
Created by:
Fullerton, Christopher
Created:
14th December, 2011, 17:00:29
Last modified by:
Fullerton, Christopher
Last modified:
16th April, 2012, 18:45:16

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