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Limit Theorems for Classical Spin Systems with an Abelian Discrete Symmetry


Caticha Alfonso, Nestor (1985) Limit Theorems for Classical Spin Systems with an Abelian Discrete Symmetry. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/yyxh-p706.


Classical spin models with a discrete abelian symmetry (Zp) are studied and compared to analogous models with a continuous (0(2)) symmetry.

The dependence on p (the number of states) of some quantities, e.g ., the pressure and correlation functions, is studied. For high p, under fairly general conditions, the pressure of the Zp invariant model converges exponentially, in p, to that of the 0(2) model. Results of a similar nature, although obtained under more restrictive conditions, are presented for a class of expectation values.

Several different methods of proving Mermin- and Wagner-like results are reviewed and it is suggested that these methods are not sufficiently powerful to be used in obtaining upper bounds on the magnetization temperature of the two dimensional Zp model. A rigorous lower bound is obtained using a Peierls-Chessboard method.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Simon, Barry M.
Thesis Committee:
  • Simon, Barry M. (chair)
  • Peck, Charles W.
  • Cross, Michael Clifford
  • Preskill, John P.
Defense Date:9 October 1984
Record Number:CaltechTHESIS:01222019-093733020
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11348
Deposited By: Mel Ray
Deposited On:28 Jan 2019 22:04
Last Modified:16 Apr 2021 22:12

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