Surface phases and surface phase transitions: A renormalization-group calculation
Švrakić, Nenad
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https://hdl.handle.net/2142/25553
Description
Title
Surface phases and surface phase transitions: A renormalization-group calculation
Author(s)
Švrakić, Nenad
Issue Date
1979
Doctoral Committee Chair(s)
Wortis, M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
surface phases
surface phase transition
renormalization group calculation
Ising model
Language
en
Abstract
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.
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