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., condmat/0306108] that the optimal scaling of localupdate flathistogram 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 localupdate 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 WangLandau algorithm. In combination with a rejection free update method, such as the Nfold way, a further significant reduction of the prefactor in the scaling can be achieved.
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MARV38011T