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Use the clustering algorithm (see Example 11

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Use the clustering algorithm (see Example 11.6) or, if you prefer, the Metropolis algorithm (see Example 11.4), to simulate the two-dimensional Ising model as described in Section 10.4. Compute the mean and variance of the energy and magnetisation per spin. (When using the clustering algorithm you should use the absolute magnetisation below the critical point because the clustering algorithm restores ergodicity which is broken in real magnets and by Metropolis.)