Correlation length in a generalized two-dimensional XY model

TL;DR

This paper investigates the magnetic and nematic correlation lengths in a generalized 2D XY model using Monte Carlo simulations, revealing their effectiveness in analyzing phase transitions and the tricritical region.

Contribution

It provides a detailed analysis of correlation lengths in a generalized XY model, offering new insights into phase transitions and the tricritical point behavior.

Findings

Correlation lengths help distinguish different phase transitions.

Magnetic correlation length reveals insights into the tricritical region.

The ratio of correlation length to lattice size exhibits distinctive behaviors.

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.