Phase diagram of generalized fully frustrated XY model in two dimensions

TL;DR

This paper explores the complex phase diagram of a two-dimensional generalized fully frustrated XY model, revealing a crossing of chirality and KT transitions, a stable phase with finite helicity modulus, and the nature of the transition lines through Monte Carlo simulations.

Contribution

It provides the first detailed analysis of the phase diagram, identifying the crossing point of chirality and KT transitions and characterizing the stability of phases in the model.

Findings

Identification of a crossing point of chirality and KT transitions.

Existence of a stable phase with finite helicity modulus.

Transition line changes from continuous to first-order.

Abstract

It is shown that the phase diagram of the two-dimensional generalized fully-frustrated XY model on a square lattice contains a crossing of the chirality transition and the Kosterlitz-Thouless (KT) transition, as well as a stable phase characterized by a finite helicity modulus $\Upsilon$ and an unbroken chirality symmetry. The crossing point itself is consistent with a critical point without any jump in $\Upsilon$, with the size ($L$) scaling $% \Upsilon\sim L^{-0.63}$ and the critical index $\nu\approx0.77$. The KT transition line remains continuous beyond the crossing but eventually turns into a first-order line. The results are established using Monte-Carlo simulations of the staggered magnetization, helicity modulus, and the fourth-order helicity modulus.