2026-09-20T03:30:28Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/25569 2023-07-10 col_2142_8859 col_2142_5131 com_2142_8858 com_2142_234 com_2142_5130

McMillan, W.L. Sears, Mark Patrick 2011-06-29T15:42:30Z 2011-06-29T15:42:30Z 10000-01-01 1979 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. Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-06-29T15:42:30Z No. of bitstreams: 1 1979_sears.pdf: 1917294 bytes, checksum: 5e69e69677d17f34ade2f297a2ccdf2c (MD5) Made available in DSpace on 2011-06-29T15:42:30Z (GMT). No. of bitstreams: 1 1979_sears.pdf: 1917294 bytes, checksum: 5e69e69677d17f34ade2f297a2ccdf2c (MD5) Previous issue date: 1979 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-06-29T15:42:30Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:19:11-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis Thesis U of I Only 361033 http://hdl.handle.net/2142/25569 en 1979 Mark Patrick Sears n-vector charged n-vector screening approximations critical behavior Green's function infrared divergences Critical behavior of the n-vector and charged n-vector models from an exact solution to the screening approximation Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.