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Title:  Numerical studies of phase transitions and critical phenomena in fermionic and polymeric systems 
Author(s):  Cannon, Joel W. 
Doctoral Committee Chair(s):  Fradkin, Eduardo H. 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Physics, Condensed Matter 
Abstract:  In this thesis we study three problems in phase transitions and critical phenomena. We study the phase diagram of the Hubbard model using montecarlo simulation, and a novel application of the Lanczos algorithm. We demonstrate the presence of a tricritical point, and estimate the phase boundary to occur at roughly V = 2.92 $\pm$.01 at U = 5.5, and V = 1.65 $\pm$.05 at U = 3.0. We estimate the tricritical point to occur above U = 3.0. We study the finitesized dependence of the energy of the ground and first excited states for various values of U to observe the crossover of the conformal anomaly, c, from free fermion to Heisenberg behavior. We have inferred c along this line using the finitesized dependence of the ground state energy. We obtain the correct asymptotic values, but find a maximum in the value of c at approximately U = 2 in apparent contradiction to Zamolodchikov's "c theorem". We show that this behavior is explained by postulating that our trajectory slices the RG trajectory in such a way that we retrace the irrelevant operators back on their trajectories for a short distance, and the presence of these operators invalidates the equation$$E\sb0(N) = E\sb{0}(\infty)  {\pi cv\sb{f}\over 6}{1\over N\sp2}\eqno(0.1)$$ We calculate the probability distribution functions for linear, 3, and 4star polymers and find that the configurations become less prolate and more anisotropic as the number of rays increase. We find that the parameterization developed by Aronovitz and Nelson is a useful and consistent way of characterizing polymer shape. I have for the first time used ground state eigenvectors, calculated with the Lanczos algorithm, to define probability distribution functions for the order parameter of a system. Algorithmic improvements include: (i) development of an efficient data structure for performing montecarlo simulations on discrete systems; (ii) A method to obtain the ground state eigenvector via the Lanczos method with a small increase in required memory; (iii) A data structure to allow efficient montecarlo simulation of a lattice polymer; and (iv) An algorithm for simulation of crosslinked polymers. In addition, we obtain numerical solutions for the ground state of the finite size Bethe ansatz equations for the Hubbard model. (Abstract shortened with permission of author.) 
Issue Date:  1989 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/19638 
Rights Information:  Copyright 1989 Cannon, Joel W. 
Date Available in IDEALS:  20110507 
Identifier in Online Catalog:  AAI9010815 
OCLC Identifier:  (UMI)AAI9010815 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Physics
Dissertations in Physics