Critical behavior of the random-bond clock model

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Critical behavior of the random-bond clock model

 

Author: Wu, Pak Hong Raymond
Title: Critical behavior of the random-bond clock model
Degree: M.Phil.
Year: 2013
Subject: Mathematical physics.
Hong Kong Polytechnic University -- Dissertations
Department: Dept. of Applied Physics
Pages: 91 leaves : ill. ; 30 cm.
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b2639223
URI: http://theses.lib.polyu.edu.hk/handle/200/7091
Abstract: The critical behavior of the clock model in two-dimensional square lattice is studied numerically using Monte Carlo method with Wolff algorithm. The Kosterlitz-Thouless (KT) transition is observed in the six-state clock model, where an intermediate phase exists between the low-temperature ordered phase and the high-temperature disordered phase. The bond randomness is introduced to the system by assuming a Gaussian distribution for the coupling coefficients with the mean μ=1 and different values of variance, from σ²=0.1 to σ²=3.0. An abrupt jump in the helicity modulus at the transition, which is the key characteristic of the KT transition, is verified with a stability argument. The critical temperature Tc for both pure and disordered systems is determined from the critical exponent η(Tc)=1/4. The results showed that a small amount of disorder (small σ) reduces the critical temperature of the system, without altering the nature of transition. However, a larger amount of disorder changes the transition from the KT-type into that of non-KT-type.

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