Unconventional phase transitions in the classical J1-J2 XY antiferromagnets on the kagome lattice

$\ $The nearest-neighbor classical antiferromagnetic $XY$ model on the kagome lattice is a fundamental model that exhibits strong geometric frustration, and its ground state is macroscopically degenerate. At zero temperature, the weak next-nearest-neighbor interaction $J_2$ lifts the degeneracy, and $q=0$ and $\sqrt3\times\sqrt3$ magnetic orders emerge [1]. On the other hand, at $J_2=0$, there is a BKT transition. However, due to numerical difficulties, it remains a non-trivial problem what kind of thermodynamic phases appear at finite temperatures under the presence of $J_2.$
$\ $In this study, the $J_2-T$ phase diagram of the model is precisely determined by large-scale classical Monte Carlo calculations using the loop update [2,3]. At zero temperature, there exists a quasi-long-range order with a $q=0$ structure in the antiferromagnetic $J_2 $region ($J_2/J_1<0$) and a $\sqrt3\times\sqrt3$ structure in the ferromagnetic $J_2 $ region ($J_2/J_1>0$). At finite temperature, we found two characteristic behaviors that have not been seen in the classical antiferromagnetic $XY$ model on the related triangular lattice.
$\ $First, we found an octupole quasi-range-ordered phase without the spin chirality ordering as an intermediate phase between the$q=0$ and $\sqrt3\times\sqrt3$ phases in the region where $|J_2/J_1 |$ is very small ($-0.005 < J_2/J_1< 0.02$).
$\ $Second, we found a first-order transition at the phase boundary between the $q=0$ and the paramagnetic phases. The first-order transition line ends at a multicritical point.
$\ $In this talk, we will discuss the relationship between these characteristic phase structures and the macroscopic degeneracy at $J_2=0.$ We will also discuss the separation of the quasi-range magnetic order from the spin chirality order.

[1] A. Harris, C. Kallin and A. Berlinsky, PRB 45, 2899 (1992)
[2] S. Schnabel and D. P Landau, PRB 86, 014413 (2012)
[3] F.Kakizawa, Finite-temperature phase diagram of the J1-J2 classical Heisenberg antiferromagnet on the kagome lattice, JPS 2020 Autumn Meeting, 10pC1-7