Scaling of emergent symmetry at a first-order transition in the simplest classical model

Emergent symmetry has attracted attention due to its possible connections with deconfined quantum criticality, where the phase boundary between a dimerized and a Neel phase is generically continuous, contrary to the standard Ginzburgb-Landau picture where a first-order phase transition is predicted.
While emergent symmetries of multicritical points have been studied in various ways ^[1], less is known about how the emergent symmetry remains at the first-order transition line starting from such multicritical points ^[2].

In this study, we analyze a simple model with two competing orders, by extensive Monte-Carlo simulation. The model has three phases (one paramagnetic and two Z₂ symmetry-breaking phases) when varying the temperature and a parameter in the Hamiltonian. We observe that the bicritical point where the three phases meet has emergent O(2) symmetry, as predicted by field-theory ^[1]. Furthermore, we find that the first-order transition line separating two ordered phases has a remainder of the emergent symmetry up to a certain length scale. We quantitatively discuss how this length scale diverges.

[1] A. Eichhorn et. al., Phys. Rev. E 88, 042141 (2013)
[2] B. Zhao, P. Weinberg, and A. W. Sandvik, arXiv:1804.07115