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 new and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We 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
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics