We study by large-scale Monte Carlo simulation the
RP3 model, which can be regarded as an effective low-energy model of a triangular lattice Heisenberg antiferromagnet.
Z2 vortices appear as elementary excitations in the triangular lattice Heisenberg antiferromagnet. Such
Z2 vortices are ubiquitous in other frustrated Heisenberg spin systems that have noncollinear long-range orders. In this study, we investigate a possible topological phase transition driven by the binding--unbinding of
Z2 vortices. By extracting important degrees of freedom, we map a frustrated spin system to an effective
RP3 model. From large-scale Monte Carlo simulation, we obtain an order parameter and a correlation length of up to
L=16384. Concerning the existence of a
Z2-vortex transition, by extrapolating the order parameter to the thermodynamics limit assuming the
Z2-vortex transition, we obtain a finite transition temperature as
Tv/J~≃0.25. Our estimate of the correlation length at
Tv is much larger than
L=16384, which is beyond the previous estimate obtained with the triangular lattice Heisenberg model.
Two-dimensional generalized XY spin model on a triangular lattice is studied by means of Monte-Carlo simulations. The critical temperatures of Berezinskii-Kosterlitz-Thouless (BKT) phase transition are obtained by the method of helicity modulus. It is found that the results are consistent with those obtained by other methods. The vortex density and the vortex-antivortex pair formation energy are also obtained. The result shows that the critical temperature decreases with the increase of the generalization parameter q . While the vortex-antivortex pair formation energy increases with the increase of q when q>1 .
Dirac fermions in (2 + 1) dimensions with dynamically generated anticommuting SO(3) antiferromagnetic and
Z2 Kekul\'e valence-bond solid (KVBS) masses map onto a field theory with a topological $\ensuremath{\theta}$ term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The $\ensuremath{\theta}$ term implies that a domain wall of the
Z2 KVBS order parameter harbors a spin-
1/2 Heisenberg chain, as described by a (1 + 1)-dimensional SO(3) nonlinear sigma model with $\ensuremath{\theta}$ term at $\ensuremath{\theta}=\ensuremath{\pi}$. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-
1/2 chain at the
Z2 topological defect. Surprisingly, the consequences of the topological term are seen far from the critical point such that the physics of apparently unrelated model systems are naturally understood by invoking them. This concept can be generalized to higher dimensions where (2 + 1)-dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.
We study a Berezinskii-Kosterlitz-Thouless-like phase transition in a triangular-lattice three-spin interaction model. The vector sine-Gordon field theory describes defects involved, and enables us to perform the renormalization-group analysis of the transition. Based on it, we discuss properties of the spin-spin correlation function, and also analyze the helicity modulus for the present model. To provide the data to support our analysis, we perform the Monte-Carlo simulations to calculate them. Further, we exhibit snapshots of some typical defect conflgurations, which are helpful to illustrate the defect-mediated phase transition.
The two-dimensional planar rotator and XY ferromagnetic models for finite lattice sizes (triangular network), with free and periodic boundary conditions, have been studied using Monte Carlo simulations. Thermodynamic quantities, suitable for comparison with experimental data, have been obtained. Heat capacity data are almost insensitive to the lattice size and to the type of boundary conditions, whereas susceptibility data are sensitive to both the lattice size and the boundary conditions. For the Kosterlitz-Thouless phase transition non-universal critical parameters are inferred. They depend on the lattice, the model and the boundary conditions. It is conjectured that the main differences between free and periodic boundary conditions are caused by the influence of the free surface on vortex energetics.
A new critical point is established through Monte Carlo simulations for a class of two dimensional XY models with a modified nearest-neighbor spin interaction. The critical exponents found are \ensuremath{\nu}\ensuremath{\approxeq}1.4, \ensuremath{\beta}\ensuremath{\approxeq}0.6, and an \ensuremath{\alpha}0, consistent with hyperscaling. The phase transition is interpreted as a vortex-unbinding transition. Comparisons are made with the phase diagram of the two dimensional Coulomb gas and with the spin-1/2 XY model.