Multicanonical multigrid Monte Carlo method

To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the d-dimensional Φ⁴ field theory in two different situations. First, we study quantum tunneling for d=1 in the continuum limit, and second, we investigate first-order phase transitions for d=2 in the infinite volume limit. Compared with standard multicanonical simulations we obtain improvement factors of several, and of about one order of magnitude, respectively.