We carry out a high-precision Monte Carlo simulation of the two-dimensional O(3)-invariant σ model at correlation lengths ξ up to ∼105. Our work employs a powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is 25% at ξ∼102, decreases to 4% at ξ∼105.
ASJC Scopus subject areas
- Physics and Astronomy(all)