Determine whether a narrow intermediate nematic phase exists near the multicritical region

Determine whether the two-dimensional generalized XY model has a very narrow intermediate nematic region in the parameter interval \(\Delta\simeq 0.34\text{--}0.36\), below the resolution of the reported parameter scan, between the half-BKT and Ising transition lines before their apparent merger with the ordinary BKT line.

Background

The HOTRG results indicate that the half-BKT and Ising transition lines may merge near $\Delta\sim 0.34$, followed by a merger of the Ising line with the ordinary BKT line near $\Delta=0.36(2)$. However, the transition lines become increasingly difficult to resolve in the interval $\Delta\simeq0.34\text{--}0.36$.

The authors state that their available data are compatible with a direct merging scenario but do not exclude a very narrow nematic phase that is too small to resolve in the present parameter scan. Consequently, whether the apparent sequential merging is a genuine direct merger or conceals an intermediate nematic region remains unresolved.