Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice

TL;DR

This study investigates the phase transitions in the frustrated six-state clock model on a triangular lattice, revealing an Ising transition for chirality and a Kosterlitz-Thouless transition for spin correlations, aligning with experimental observations.

Contribution

It provides a detailed Monte Carlo analysis of the model's two distinct phase transitions and connects theoretical results with experimental data.

Findings

Chirality order sets in below a critical temperature in the Ising universality class.

Spin correlations decay algebraically below the KT transition temperature.

The model captures the universal features observed in experimental orientational ordering.

Abstract

We study the anti-ferromagnetic six-state clock model with nearest neighbor interactions on a triangular lattice with extensive Monte-Carlo simulations. We find clear indications of two phase transitions at two different temperatures: Below $T_I$ a chirality order sets in and by a thorough finite size scaling analysis of the specific heat and the chirality correlation length we show that this transition is in the Ising universality class (with a non-vanishing chirality order parameter below $T_I$). At $T_{KT}(<T_I)$ the spin-spin correlation length as well as the spin susceptibility diverges according to a Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below $T_{KT}$. We compare our results to recent x-ray diffraction experiments on the orientational ordering of CF$_3$Br monolayers physisorbed on graphite. We argue that the six-state clock model describes the universal feature of the phase transition in the experimental system and that the orientational ordering belongs to the KT universality class.