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 $\beta =\infty$. 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 $q\to 0$ and $\omega \to 0$ can be approached directly. As examples we calculate spectra for the $d=2\mathrm{}$ Ising model and for Heisenberg quantum spin ladders with two and four legs.