UCL Discovery

## Extrapolating Monte Carlo Simulations to Infinite Volume: Finite-Size Scaling at ξ/L ≫1

Caracciolo, S; Edwards, RG; Ferreira, SJ; Pelissetto, A; Sokal, AD; (1994) Extrapolating Monte Carlo Simulations to Infinite Volume: Finite-Size Scaling at ξ/L ≫1. Physical Review Letters , 74 (15) 2969 - 2972. 10.1103/PhysRevLett.74.2969.

## 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.

Type: Article Extrapolating Monte Carlo Simulations to Infinite Volume: Finite-Size Scaling at ξ/L ≫1 An open access version is available from UCL Discovery 10.1103/PhysRevLett.74.2969 http://dx.doi.org/10.1103/PhysRevLett.74.2969 © 1995 The American Physical Society UCLUCL > Provost and Vice Provost OfficesUCL > Provost and Vice Provost Offices > UCL BEAMSUCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical SciencesUCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics https://discovery.ucl.ac.uk/id/eprint/1323422