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We study the ordering of the spin and the chirality in the fully frustrated XY model on a square lattice by extensive Monte Carlo simulations. Our results indicate unambiguously that the spin and the chirality exhibit separate phase transitions at two distinct temperatures, i. e. , the occurrence of the spin-chirality decoupling. The chirality exhibits a long-range order at T_c=0.45324(1) via a second-order phase transition, where the spin remains disordered with a finite correlation length xi_s(T_c) sim 120. The critical properties of the chiral transition determined from a finite-size scaling analysis for large enough systems of linear size L > xi_s(T_c) are well compatible with the Ising universality. On the other hand, the spin exhibits a phase transition at a lower temperature T_s=0.4418(5) into the quasi-long-range-ordered phase. We found eta(T_s)=0.201(1), suggesting that the universality of the spin transition is different from that of the conventional Kosterlitz-Thouless (KT) transition.
The two-dimensional ($2d$) fully frustrated Planar Rotator model on a square lattice has been the subject of a long controversy due to the simultaneous $Z_2$ and $O(2)$ symmetry existing in the model. The $O(2)$ symmetry being responsible for the Ber
The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of Q by const
Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change
We investigate the coarsening dynamics in the two-dimensional Hamiltonian XY model on a square lattice, beginning with a random state with a specified potential energy and zero kinetic energy. Coarsening of the system proceeds via an increase in the
We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gauss