1. 2007.4.19~20 Monte Carlo Study of the J 1 -J 2 antiferromagnetic XY model on the triangular lattice Department of Physics Sungkyunkwan University Jin-Hong Park and Jung Hoon Han

2. Two types of the transition found on triangular lattice Classical XY model Hamiltonian. XY model on triangular lattice 1.Kosterlitz-Thouless(KT) transition 2.Chirality transition

3. The separation of the phase temperatures is extremely small. The chirality-ordered phase is not well-defined. Sooyeul Lee and Koo-Chul Lee, Phys. Rev. B 57, 8472 (1998) T Magnetic Paramagnetic T KT T   XY model on triangular lattice - + + ++ + + + + + - - --- --- Chiral

4. Biquadratic interaction on triangular lattice ? Biquadratic interaction on triangular lattice ? If the spin-spin interaction is biquadratic, a spin-nematic order is realized instead.. Biquadratic interaction supports a spin nematic order. =or

5. We want to study a variant of the XY model in which the chirality order exists over an extended region of the phase diagram by combining quadratic and bi-quadratic interactions J 1 -J 2 XY model J 2 /J 1 T paramagnetic magnetic chiral, non- magnetic J 2 /J 1 =9 We focus on J 2 /J 1 = 9. A chiral phase is seen to exist over an extended temperature region when J 2 /J 1 is large

6. T1T1T1T1 T2T2T2T2 J 2 /J 1 = 9 (L = 15, 30, 60). Specific heat Two phase transitions clearly identified

7. Magnetic order parameter Nematic order parameter Magnetic/nematic parameters We study the nature of the phases with the magnetic and nematic order parameters

8. Chiral order parameter + - 1 3 2 4

9. Magnetic order

10. Binder cumulent Nematic order T KT = 0.460

11. Helicity Modulus Helicity modulus. T KT = 0.459 This T KT must agree with the one obtained from Binder cumulent in the previous page.

12. critical disorder T KT Critical phase for nematic order below T KT We find critical dependence of N 1 and N 2 on the lattice dimension L below T KT.

13. Chiral order Chiral order undergoes two phase transitions. The first one at higher temperature obeys a scaling plot. A scaling plot of chirality using the  0.15,  0.69, and T  = 0.462. This T  is higher than T KT of the nematic order.

14. T MagneticChiralParamagnetic T Magnetic Paramagnetic Phase diagram J 2 /J 1 =0 J 2 /J 1 =9 By introducing frustration in the form of J 2 we find an extended region of chiral phase

15. 1.We find a clear separation of magnetic (T 1 ) and nematic (T 2 ) phase transition for J 2 /J 1 = 9. 3.This is the first demonstration of the clear separation of the chiral phase transition and the magnetic phase transition in XY-like models. Summary 2.Quite remarkably, the staggered chirality order sets in at T=T 2, where the nematic order occurs. the nematic order occurs.

16. Appendix +1