Algorithmic overlaps in the Baxter–Wu model: cluster dynamics under Novotny–Evertz updates

Nuclear Physics B. 2026. No. 0550-3213. Article 117706.

Pilé I., Shchur L.

We study the spatial overlap of successive spin configurations generated by Markov chain Monte Carlo simulations of the Baxter–Wu model. Using the Novotny–Evertz sublattice-freezing single-cluster update, we track the mean and variance of the algorithmic overlap across the critical region. We show that, even in this three-spin model, the overlap acts as an algorithmic observable that follows the thermodynamics of the transition: the single-cluster overlap mean behaves like an order parameter, dropping from a finite ordered-phase plateau toward zero across Tc. The overlap does not diverge at criticality, instead it remains finite and its finite-size value decays as a clean power law, U2(Tc)∼L−ψ, over eleven sizes with an exponent ψ=0.378(4). The exponent is stable under removal of small and large sizes and under the correction-to-scaling terms known for this model, which enter with amplitudes consistent with zero. It differs by more than eight standard errors from the values found for the Ising, three-state Potts and four-state Potts models under standard Fortuin–Kasteleyn Wolff dynamics. The Novotny–Evertz clusters reproduce the susceptibility exponent γ/ν=7/4, which the Ising model shares, so the difference is not set by the static exponents or by the cluster-size exponent.

Keywords: Monte-Carlo, Finite-size scaling, critical phenomena, configuration overlaps, Cluster algorithms