After a brief general overview of Monte Carlo computer simulations in
statistical physics, special emphasis is placed on applications to pha
se transitions and critical phenomena. Here, standard simulations empl
oying local update algorithms are severely hampered by the problem of
critical slowing down, that is by strong correlations between successi
vely generated data It is shown that this problem can be greatly reduc
ed by using nonlocal update techniques such as cluster and multigrid a
lgorithms. The general ideas are illustrated for simple lattice spin m
odels and Euclidean path integrals. (C) 1998 IMACS/ Elsevier Science B
.V.