Criticality of the loop O(2) model at the predicted transition point

Establish whether the loop $O(2)$ model is critical at $(n,x)=(2,1/\sqrt{2})$.

Background

The paper proves that translation-invariant Gibbs measures for the loop $O(n)$ model have infinitely many loops surrounding every face throughout $n\in[1,2]$ and $x\in[1/\sqrt{2},1]$. It specifically identifies the endpoint $(2,1/\sqrt{2})$ as a conjecturally critical point, making its criticality an unresolved question distinct from the broader conjecture about the phase diagram.