Non-trivial \theta-Vacuum Effects in the 2-d O(3) Model

TL;DR

This study investigates the effects of -vacua in the 2-dimensional lattice O(3) model, demonstrating that different  values lead to distinct continuum theories and confirming the exact S-matrix at  =  through precise Monte Carlo simulations.

Contribution

The paper introduces an optimized constraint action that minimizes cut-off effects, enabling accurate analysis of -vacua effects and confirming theoretical predictions at  = .

Findings

Dislocation lattice artifacts do not prevent the non-trivial continuum limit at  non-zero.

Different continuum theories emerge for each  value.

Monte Carlo results confirm the exact S-matrix at  = .

Abstract

We study \theta-vacua in the 2-d lattice O(3) model using the standard action and an optimized constraint action with very small cut-off effects, combined with the geometric topological charge. Remarkably, dislocation lattice artifacts do not spoil the non-trivial continuum limit at \theta\ non-zero, and there are different continuum theories for each value of \theta. A very precise Monte Carlo study of the step scaling function indirectly confirms the exact S-matrix of the 2-d O(3) model at \theta = \pi.