MULTICANONICAL MONTE-CARLO SIMULATIONS

Canonical Monte Carlo simulations of disordered systems like spin glas ses and systems undergoing first-order phase transitions are severely hampered by rare event states which lead to exponentially diverging au tocorrelation times with increasing system size and hence to exponenti ally large statistical errors. One possibility to overcome this proble m is the multicanonical reweighting method. Using standard local updat e algorithms it could be demonstrated that the dependence of autocorre lation times on the system size V is well described by a less divergen t power law, tau proportional to V-alpha, with 1 < alpha < 3, dependin g on the system. After a brief review of the basic ideas, combinations of multicanonical reweighting with non-local update algorithms will b e discussed. With the multibondic algorithm, which combines multicanon ical reweighting with cluster updates, the dynamical exponent alpha ca n be reduced to unity, the optimal value one would expect from a rando m walk argument. Asymptotically for large system sizes the multibondic algorithm therefore always performs better than the standard multican onical method. Finally it is shown that a combination with multigrid u pdate techniques improves the performance of multicanonical simulation s by roughly one order of magnitude, uniformly for all system sizes. ( C) 1998 Elsevier Science B.V. All rights reserved.