# Phase Diagram of a Generalized XY Model with Geometrical Frustration

## TL;DR

This study explores how geometrical frustration affects a generalized XY model with antiferromagnetic and antinematic interactions on a triangular lattice, revealing a rich phase diagram with multiple quasi-long-range ordered phases.

## Contribution

It introduces a generalized XY model with a third-order antinematic term and maps out its complex phase diagram, highlighting new noncollinear QLRO phases due to frustration.

## Key findings

- Identification of three distinct QLRO phases at finite temperatures.
- Discovery of a new noncollinear QLRO phase between AFM and AN3 phases.
- Comparison showing the generalized model's richer phase structure than the AN2 case.

## Abstract

In the present study we investigate the effects of geometrical frustration on the XY model with antiferromagnetic (AFM) coupling on a triangular lattice, generalized by the inclusion of a third-order antinematic term (AN3). We demonstrate that at non-zero temperatures such a generalization leads to a phase diagram consisting of three different quasi-long-range ordered (QLRO) phases. Compared to the model with the second-order AN coupling (AN2), it includes besides the AFM and AN3 phases which appear in the limits of relatively strong AFM and AN3 interactions, respectively, an additional complex noncollinear QLRO phase at lower temperatures wedged between the AFM and AN3 phases. This new phase originates from the competition between the AFM and AN3 couplings, which is absent in the model with the AN2 coupling.