The two-phase issue in the O(n) non-linear $\sigma$-model: A Monte Carlo study

Abstract

We have performed a high statistics Monte Carlo simulation to investigate whether the two-dimensional O(n) non-linear sigma models are asymptotically free or they show a Kosterlitz- Thouless-like phase transition. We have calculated the mass gap and the magnetic susceptibility in the O(8) model with standard action and the O(3) model with Symanzik action. Our results for O(8) support the asymptotic freedom scenario.

3 pgs. espcrc2.sty included. Talk presented at LATTICE96(other models)

References in corpus (3)

• Asymptotic Scaling in the Two-Dimensional $O(3)$ $\sigma$-Model at Correlation Length $10^5$
• Asymptotic scaling in the two-dimensional $SU(3)$ $\sigma$-model at correlation length $4\times 10^5$
• Four-Loop Perturbative Expansion for the Lattice $N$-Vector Model

Cited by in corpus (5)

• Corrections to Finite-Size Scaling in the Lattice N-Vector Model for Infinite N
• Two-Dimensional Heisenberg Model with Nonlinear Interactions
• Four-loop contributions to long-distance quantities in the two-dimensional nonlinear sigma-model on a square lattice: revised numerical estimates
• Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections
• Asymptotic Freedom and Finite-size Scaling of Two-dimensional Classical Heisenberg Model