Determine the long-distance behavior of the axial-field correlator

Determine whether the two-point correlation function of the Lagrange-multiplier field \(\theta\) in Jacobson’s four-dimensional no-intersection model approaches a clear nonzero long-distance plateau in the small-coupling regime.

Background

Jacobson’s no-intersection model contains a Lagrange-multiplier field $\theta$ associated with the axial $U(1)_A$ symmetry, although $\theta$ is integrated out in the simulations to avoid the sign problem. Its two-point function can nevertheless be measured using defect-propagation updates. At $\kappa=0.02$, the correlator’s tail increases with lattice size, which could indicate long-range order, but the authors do not observe a definite plateau. Establishing its asymptotic behavior is important for determining whether the axial symmetry is spontaneously broken and how the anomaly is realized.