Topics in Statistic Mechanics
Topics in Statistic Mechanics
Topics in Statistic Mechanics
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Adv. Sta. Phy.Homework 3 Is<strong>in</strong>g Model Li,Zimeng PB06203182<br />
Fig 12<br />
2. The exact solution of the critical po<strong>in</strong>t on the square lattice<br />
We def<strong>in</strong>e our effective Hamiltonian as<br />
We <strong>in</strong>troduce <strong>in</strong> the follow<strong>in</strong>g variables:<br />
We have ( )<br />
Therefore<br />
=<br />
So<br />
We here <strong>in</strong>troduce <strong>in</strong> the Bragg-Williams method<br />
We def<strong>in</strong>e<br />
and<br />
We therefore rewrite the effective Hamiltonian as<br />
We suppose
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