Last updated: Feb 12, 2001


Introduction

The multicanonical (MUCA) Monte Carlo (MC) method calculates expectation values of the Gibbs ensemble for a desired temperature range. The subsequent figure depicts histograms from Gibbs canonical and multicanonical MC simulations of the 2d Ising model on an 80x80 lattice at temperature T=1/beta. The canonical simulations were carried out at beta=0 and beta=0.4. The multicanonical simulation covered the range beta=0 to beta=0.449.

The original papers are PLB 267 (1991) 249 and PRL 68 (1992) 9 (both with Neuhaus). The first application to complex system is given in PRL 69 (1992) 2292 (with Celik). Detailed references are given in my review article cond-mat/9909236 (published in the Fields Institute Communications 26 (2000) 1-24).

Conventional, canonical MC simulations sample with the Boltzmann weight

exp [ - beta E ]


where E is the energy of the system. MUCA simulations sample with a weight function

exp [ - b(E) E + a(E) ]


which needs to be determined recursively. The fugacity a(E) follows from b(E) which is related to the microcanonical temperature T(E) by

b(E) = 1 / T(E)


and the simulated MUCA temperature range is, essentially, determined by the extrema of T(E). A recursive estimate of b(E) is therefore necessary before the proper MUCA simulation can begin. With respect to this progress has been made in recent years. The following link


Multicanonical Recursion

leads to an exposition a recursion described in the above mentioned review article.

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