We study critical properties of the Kitaev-Heisenberg model on the honeycomb lattice at finite temperatures which might describe the physics of the quasi two-dimensional compounds, Na2IrO3 and Li2IrO3. The model undergoes two phase transitions as a function of temperature. At low temperature, thermal fluctuations induce magnetic long-range order by order-by-disorder mechanism. Magnetically ordered state with the spontaneously broken Z6 symmetry persists up to a certain critical temperature. We find that there is an intermediate phase between the low-temperature ordered phase and the high-temperature disordered phase. The finite-sized scaling analysis suggests that the intermediate phase is a critical Kosterlitz-Thouless phase with continuously variable exponents. We argue that the intermediate phase has been actually observed above the low-temperature magnetically ordered phase in Na2IrO3, and likely in Li2IrO3.
@article{arxiv.1205.3967,
title = {Critical properties of the Kitaev-Heisenberg model},
author = {Craig Price and Natalia B. Perkins},
journal= {arXiv preprint arXiv:1205.3967},
year = {2015}
}