Critical behavior of the n-vector and charged n-vector models from an exact solution to the screening approximation
Sears, Mark Patrick
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https://hdl.handle.net/2142/25569
Description
Title
Critical behavior of the n-vector and charged n-vector models from an exact solution to the screening approximation
Author(s)
Sears, Mark Patrick
Issue Date
1979
Doctoral Committee Chair(s)
McMillan, W.L.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
n-vector
charged n-vector
screening approximations
critical behavior
Green's function
infrared divergences
Language
en
Abstract
Within the screening approximation the n-vector 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 n-vector model, which consists of the ordinary n-vector 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.
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