Simulations on infinite-size lattices

We introduce a Monte Carlo method. as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta = infinity. All two-point functions can be obtained, including dynamical information. When the number of iterations is increased, correlation functions at larger distances become available. Limits q --> 0 and omega --> 0 can be approached directly. As examples we calculate spectra for the d = 2 using model and for Heisenberg quantum spin ladders with two and four legs.