Multicanonical Monte Carlo simulations

Canonical Monte Carlo simulations of disordered systems like spin glasses and systems undergoing first-order phase transitions are severely hampered by rare event states which lead to exponentially diverging autocorrelation times with increasing system size and hence to exponentially large statistical errors. One possibility to overcome this problem is the multicanonical reweighting method. Using standard local update algorithms it could be demonstrated that the dependence of autocorrelation times on the system size V is well described by a less divergent power law, τ∝Vα, with 1<α<3, depending on the system. After a brief review of the basic ideas, combinations of multicanonical reweighting with non-local update algorithms will be discussed. With the multibondic algorithm, which combines multicanonical reweighting with cluster updates, the dynamical exponent α can be reduced to unity, the optimal value one would expect from a random walk argument. Asymptotically for large system sizes the multibondic algorithm therefore always performs better than the standard multicanonical method. Finally it is shown that a combination with multigrid update techniques improves the performance of multicanonical simulations by roughly one order of magnitude, uniformly for all system sizes.