Dissertation/Thesis Abstract

Combinatorial Monte Carlo simulations for the disordered two-dimensional dimer model
by Taha, Ahmed Gamaleldin, Ph.D., The George Washington University, 2007, 133; 3288839
Abstract (Summary)

In this work, we study the thermodynamics of the (1+1)-dimensional planar fluxline lattice in the presence of quenched disorder using a two-dimensional random bond dimer model. We use Monte Carlo simulations to generate an exact ground state and to calculate disorder averages for thermodynamic quantities including the free energy, internal energy, entropy and heat capacity.

Over a wide range of temperature and disorder strength, the effective lattice stiffness and cumulants are found to excellently agree with an analytical approach based on Replica-Symmetric Bethe Ansatz (RBA) solution. The new shuffling algorithm provides an importance sampling Monte Carlo simulation to generate over a thousand thermal samples of dimer matchings on a square lattice that are guaranteed to be statistically uncorrelated.

The lowest-lying droplet excitations are investigated in depth due to both changes in disorder and changes in temperature. We calculated the energy scaling exponent for central droplets and their fractal dimension based on their circumference as their significant length scale.

We also calculated the disorder-averaged heat capacity of the fluxline lattice by averaging the droplet excitation energy for all length scales, and also from the density of states of central droplets within a two-level system approximation. Qualitative discussions of the scope and the validity of the used approximations are given with supportive quantitative explanations.

Indexing (document details)
Advisor: Zeng, Chen
Commitee: Balbach, John J., Parke, William C., Peng, Weiqun, Reeves, Mark E., Zhang, Naigong
School: The George Washington University
Department: Physics
School Location: United States -- District of Columbia
Source: DAI-B 68/12, Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Condensation, Physics
Keywords: Combinatorial Monte Carlo, Droplet excitations, Fluxline lattices
Publication Number: 3288839
ISBN: 9780549318378
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