New Method for the Extrapolation of Finite-Size Data to Infinite Volume

Abstract

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional $O(3)$ and $O(\infty )$ $\sigma$-models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.

Comments: 3 pages, 76358 bytes Postscript, contribution to Lattice '94; see also hep-lat/9409004, hep-lat/9405015 and hep-lat/9411009