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Finite-Size Scaling at $ξ/L \gg 1$

Sergio Caracciolo·Robert G. Edwards·Sabino José Ferreira·Andrea Pelissetto·Alan D. Sokal
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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 $O(\infty)$ $σ$-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.

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Sergio Caracciolo, Robert G. Edwards, Sabino José Ferreira, Andrea Pelissetto, Alan D. Sokal. 1994-09-06. Finite-Size Scaling at $ξ/L \gg 1$. https://doi.org/10.1103/physrevlett.74.2969

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