Multibondic Cluster Algorithm for Monte Carlo Simulations of First-Order Phase Transitions

Inspired by the multicanonical approach to simulations of first-order phase transitions we propose for $q$-state Potts models a combination of cluster updates with reweighting of the bond configurations in the Fortuin-Kastelein-Swendsen-Wang representation of this model. Numerical tests for the two-dimensional models with $q=7, 10, \mathrm{and} 20$ show that the autocorrelation times of this algorithm grow with the system size $V$ as $\tau \propto V^{\alpha }$, where the exponent takes the optimal random walk value of $\alpha \approx 1$.