Is the easy-plane deconfined transition continuous?
In plain words
If the spins are restricted to rotate in a plane, the same transition may behave differently and is linked by predicted dualities to other field theories. Simulations disagree on whether it is continuous.
Precise statement
For easy-plane (U(1) x U(1) symmetric) versions of the Neel-VBS problem, such as the easy-plane $J-Q$ model or easy-plane NCCP1 lattice gauge theories, determine whether the XY-antiferromagnet to VBS transition is continuous with emergent $O(4)$ symmetry, as self-duality predicts, or first order. An answer is the order of the transition, with exponents if continuous.
What would settle it
Large-scale Monte Carlo of several easy-plane lattice realizations showing consistent order parameters and exponents at the transition.
Status in the literature
Unverified note
Easy-plane J-Q simulations show a first-order transition while other easy-plane lattice models appear continuous; a non-Hermitian deformation of the easy-plane J-Q model weakens the first-order jump, consistent with a complex-fixed-point scenario (Zou, Yin, Li, Yao, arXiv:2511.03456, 2025).