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Exercise 13.7: Critical slowing down

  1. Consider the 2D Ising model on a square lattice with $L=16$. Compute the correlation time $\tau$ for $T=1.5$, $2.4$, and $2.3$. Show that $\tau$ increases as the critical temperature is approached, a physical effect known as ``critical slowing down''.

    The magnitude of $\tau$ depend in part on our choice of ``dynamics''. Although we generate trial configurations attempting a single spin flip, it is possible to simultaneously flip two or more spins, even an entire cluster. This other update strategies are more efficient and lead to smaller correlation times.



Adrian E. Feiguin 2009-11-04