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oai:www.ideals.illinois.edu:2142/25553 2023-07-10 col_2142_8859 col_2142_5131 com_2142_8858 com_2142_234 com_2142_5130

Wortis, M. Švrakić, Nenad 2011-06-28T16:07:45Z 2011-06-28T16:07:45Z 10000-01-01 1979 The aim of this thesis is to study the surface phases, surface phase transitions, and thermodynamic properties of the semi-infinite Ising model in two and three dimensions. We show how position-space renormalization group methods, previously used in homogeneous bulk calculations, can be generalized to give surface properties. In two dimensions a 4x4 cell-cluster approximation gives critical and thermodynamic properties in quantitative agreement with the. exact results of McCoy and Wu. In three dimensions a cruder (2-cell) approximation gives results which appear in qualitative agreement with what is known. The model, although simplified, captures many features of some real physical systems. We first give a brief overview of surface thermodynamics including surface phases and phase transitions. Then, the phenomenology of the semi-infinite Ising model is outlined. Next, we briefly describe the results of some previous theoretical studies of the semi-infinite Ising model. These studies include: (i) an exact calculation in two dimensions, (ii) series expansion calculations, (iii) the mean-field theory (MFT) approach, and (iv) RG calculations including the (-expansion and position-space methods in two and three dimensions. We describe briefly the MFT approach. The major part of the thesis is devoted to the discussion of conceptual and practical aspects of the position-space renormalization-group application to the calculation of surface properties. We point out some ambiguities that arise in such a calculation when finite-cell cluster approximate recursion relations are used. In particular, we point out the influence of such modifications as boundary conditions, cell projections, etc. on the behavior of thermodynamic functions at high and low temperatures. A cluster expansion method (Ursell expansion) is used to deal with these difficulties. All of the results are listed at the end. Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-06-28T16:07:45Z No. of bitstreams: 1 1979_svrakic.pdf: 3722501 bytes, checksum: 8b1961105f5078d8bc2ae6564f783e54 (MD5) Made available in DSpace on 2011-06-28T16:07:45Z (GMT). No. of bitstreams: 1 1979_svrakic.pdf: 3722501 bytes, checksum: 8b1961105f5078d8bc2ae6564f783e54 (MD5) Previous issue date: 1979 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-06-28T16:07:45Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:32:26-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis Thesis U of I Only 409221 http://hdl.handle.net/2142/25553 en 1979 Nenad Švrakić surface phases surface phase transition renormalization group calculation Ising model Surface phases and surface phase transitions: A renormalization-group calculation Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.