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Title:  Critical behavior of the nvector and charged nvector models from an exact solution to the screening approximation 
Author(s):  Sears, Mark Patrick 
Doctoral Committee Chair(s):  McMillan, W.L. 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  nvector
charged nvector screening approximations critical behavior Green's function infrared divergences 
Abstract:  Within the screening approximation the nvector model can be solved exactly. Results for the high temperature phase are presented here. For 1arge n there is the expected agreement with the 1/n expansion results while for small n we explore the nonexistence of a solution in the regime of spatial dimension 2 < d < 4. Corrections to a previous publication are made. By keeping the dual leading corrections to the scaling Green's function we establish the correct connection between the Green's function and specific heat and demonstrate the cancellation of infrared divergences. The charged nvector model, which consists of the ordinary nvector model with a coupling to an abelian gauge field, is appropriate for the scaling regions of the superconducting pbase transition and smectic A~nematic transitions in some liquid crystals. In previous work by Halperin, Lubensky and Ma the exponents n and v were calculated to order E and to leading order in 1/n for d = 3. The calculation presented here is exact to leading order in 1/n for all d and results are given for d = 2 + E, 3 and 4 E. The results n for n agree with those of HLM, but for v a discrepancy exists, perhaps due to their neglect of n compared with the O[1/n] pieces of v. Numerical calculations for small n are also presented. For the case n = 2, d = 3 corresponding to models of physical interest solutions for n and v exist but are not expected to be at all accurate. 
Issue Date:  1979 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/25569 
Rights Information:  1979 Mark Patrick Sears 
Date Available in IDEALS:  20110629 
Identifier in Online Catalog:  361033 
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