Critical behavior of the n-vector and charged n-vector models from an exact solution to the screening approximation

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2011

Author dc:creator

• Sears, Mark Patrick

Contributors dc:contributor

• McMillan, W.L.

• n-vector
• charged n-vector
• screening approximations
• critical behavior
• Green's function
• infrared divergences

Statement dc:rights

• 1979 Mark Patrick Sears

Language dc:language

en

Identifier

361033

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/25569