Classical Origins of Landau-Incompatible Transitions

Continuous phase transitions where symmetry is spontaneously broken are ubiquitous in physics and often found between "Landau-compatible" phases where residual symmetries of one phase are a subset of the other. However, continuous "deconfined quantum critical" transitions between Landau-incompatible symmetry-breaking phases are known to exist in certain quantum systems, often with anomalous microscopic symmetries. In this Letter, we investigate the need for such special conditions. We show that Landau-incompatible transitions can be found in a family of well-known classical statistical mechanical models with anomaly-free symmetries, introduced by José et al. [Phys. Rev. B 16, 1217 (1977).PLRBAQ0556-280510.1103/PhysRevB.16.1217]. The models are anisotropic deformations of the classical 2D XY model labeled by a positive integer Q. For a range of temperatures, even Q models exhibit two Landau-incompatible partial symmetry-breaking phases and a direct transition between them for Q≥4. Characteristic features of deconfined quantum criticality, such as enhanced symmetries and melting of charged defects, are easily seen in a classical setting. For odd Q and corresponding temperature ranges, two regions of a single partial symmetry-breaking phase appear, split by a stable "unnecessary critical" line. We discuss experimental systems that realize these transitions and present anomaly-free quantum models that also exhibit similar phase diagrams.