CM In the literature: contested

Is the Neel to valence-bond-solid transition in the J-Q model continuous?

In plain words

In the J-Q model a magnetic (Neel) state turns into a state of locked spin pairs (a valence-bond solid) as a four-spin coupling grows. Simulations show slowly drifting critical exponents, so it is unclear whether the transition is continuous or a very weak jump.

Precise statement

Square-lattice $S = 1/2$ $J-Q$ model, $H = -J \sum P_{ij} - Q \sum P_{ij} P_{kl}$ with $P_{ij}$ the singlet projector, at the Neel to columnar-VBS transition $q_c = (Q/J)_c$. Determine whether both order parameters vanish continuously at $q_c$ or remain finite (first order), and if first order, the coexisting order parameters and the correlation length at $q_c$. An answer is the thermodynamic-limit order parameters at $q_c$ with error bars.

What would settle it

Quantum Monte Carlo on lattices beyond $L = 256$, or a controlled extrapolation, showing nonzero coexisting Neel and VBS order at $q_c$, or their vanishing.

Status in the literature

Unverified note

2024 to 2026 quantum Monte Carlo and spectroscopic studies (for example arXiv:2512.11329) report evidence for a weakly first-order transition with emergent SO(5) symmetry broken to O(4).