Limit Theorems for Classical Spin Systems with an Abelian Discrete Symmetry
<p>Classical spin models with a discrete abelian symmetry (Z<sub>p</sub>) are studied and compared to analogous models with a continuous (0(2)) symmetry.</p> <p>The dependence on p (the number of states) of some quantities, e.g ., the pressure and correlation functio...
| Summary: | <p>Classical spin models with a discrete abelian symmetry (Z<sub>p</sub>) are studied and compared to analogous models with a continuous (0(2)) symmetry.</p>
<p>The dependence on p (the number of states) of some quantities, e.g ., the pressure and correlation functions, is studied. For high <i>p</i>, under fairly general conditions, the pressure of the Z<sub>p</sub> invariant model converges exponentially, in <i>p</i>, 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.</p>
<p>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 Z<sub>p</sub> model. A rigorous lower bound is obtained using a Peierls-Chessboard method.</p> |
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