Feedback for speed: How fast can we calculate the density of states of classical Ising models?
Abstract
For the ferromagnetic and fully frustrated 2D Ising models we have recently shown [Dayal et al., cond-mat/0306108] that the optimal scaling of local-update flat-histogram methods with the number of spins N is not the minimal N^2 of an unbiased random walk in energy space, but a power law N^2.37, resp. N^2.86. To overcome these limitations of entropic sampling we present a novel adaptive approach which maximizes the rate of round trips of an equilibrium random walker in energy space. The scaling of tunneling times for this local-update algorithm is found to be only O([N log N]^2) for both, the ferromagnetic and the fully frustrated 2D Ising model. The novel algorithm thus outperforms other numerical approaches such as the multicanonical method and the Wang-Landau algorithm. In combination with a rejection free update method, such as the N-fold way, a further significant reduction of the prefactor in the scaling can be achieved.
- Publication:
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APS March Meeting Abstracts
- Pub Date:
- March 2004
- Bibcode:
- 2004APS..MARV38011T