Correlation length in a generalized two-dimensional XY model

Abstract

The measurements of the magnetic and nematic correlation lengths in a generalization of the two dimensional XY model on the square lattice are presented using classical Monte Carlo simulation. The full phase diagram is re-examined based on these correlation lengths, demonstrating their power in studying generalized XY models. The ratio between the correlation length and the lattice size has distinctive behaviors which can be used to distinguish different types of phase transition. More importantly, the magnetic correlation length give more insights into the tricritical region where the paramagnetic, nematic and quasi-long-range phases meet. It shows signatures for the intermediate region starting from the tricritical point, where the transition line is neither of the same physics as the Ising transition below nor the Berezinskii-Kosterlitz-Thouless transition far above the tricritical point.

10 pages, 7 figures

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• Hybrid Berezinskii-Kosterlitz-Thouless and Ising topological phase transition in the generalized two-dimensional XY model using tensor networks
• $XY$ model with antinematic interaction
• Phase diagram of generalized XY model using tensor renormalization group
• Unsupervised learning of phase transitions via modified anomaly detection with autoencoders
• Vortex confinement transitions in the modified Goldstone model
• Phase diagrams of antiferromagnetic $XY$ model on a triangular lattice with higher-order interactions
• ${\mathbb{Z}}_n$ modified XY and Goldstone models and vortex confinement transition
• Ordering kinetics and steady states of XY-model with ferromagnetic and nematic interaction