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m General fixes, replaced: = See Also = → = See also = |
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This probability distribution has been derived in the following way: the Hamiltonian of the Ising model is
<math>H[\sigma]=\sum\limits_{<i,j>}-J_{i,j}\sigma_i\sigma_j</math>,
and the [[Partition function (statistical mechanics)|partition function]] is
<math>Z=\sum\limits_{\lbrace\sigma\rbrace}e^{-\beta H[\sigma]}</math>.
Consider the interaction between a pair of selected sites <math>n</math> and <math>m</math> and eliminate it from the total Hamiltonian, defining
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Introduce the quantity
<math>Z_{nm}^{ind}=Z_{n,m}^{same}+Z_{n,m}^{diff}</math>;
the partition function can be rewritten as
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The algorithm is not efficient in simulating [[Geometrical frustration|frustrated systems]].
== See
* [[Random cluster model]]
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