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Title: Studies of structural patterns at phase transitions
Author: Wilding, Nigel Blair
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1991
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The work described in this thesis comprises two distinct components. In the first part, Monte-Carlo computer simulation methods are employed within a finite-size scaling framework to investigate both universal and non-universal behaviour in two scalar models, the 1-d φ4 model and the 2-d Lennard-Jones fluid. In both these models the properties of interest are obtained from studies of the large-length scale configurational patterns via measurements of the probability distribution function (PDF) of the coarse-grained (block) ordering variable. For the 1-d φ4 model, simulations are employed to obtain the block PDF of the spin variable. This function is shown to map onto an analytically-derived expression for the 1-d Ising chain, thus exposing the model's essentially Ising-like character. It is further demonstrated that the corrections to the limiting form of the block PDF reflect system-specific features of the 1-d φ4 model associated with its elementary excitations. In the 2-d Lennard-Jones fluid, the combined use of simulation and finite-size scaling is shown to provide a powerful method for accurately determining the location of the liquid-vapour coexistence curve and critical point. At the critical point, the limiting form of the coarse-grained density distribution is found to collapse onto a previously determined function characteristic of the 2-d Ising model, thereby confirming and clarifying fluid-magnet universality. Clear evidence is also presented for mixing of the temperature and chemical potential in the two relevant scaling fields-a phenomenon responsible for the failure of the law of rectilinear diameter. As an addendum, a discussion is given of the prospects for generalising to fluids, the cluster updating techniques recently developed to reduce critical slowing down in simulations of spin systems.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available