Role of topological defects in the phase transition of a modified XY model: a Monte Carlo study

Generalized XY model with competing antiferromagnetic and antinematic interactions

I study effects of q-order antinematic (AN_{q}) interactions on the critical behavior of the antiferromagnetic (AF) XY model on a square lattice. It is found that the evolution of the phase diagram topology of such AF-AN_{q} models with the parameter q does not follow the same line as for the corresponding FM-N_{q} models with the ferromagnetic (FM) and q-order nematic (N_{q}) interactions. Their phase diagrams are similar only for odd values of the parameter q. In such cases the respective phases reported in the FM-N_{q} models are observed in the AF-AN_{q} models on each of the two AF-coupled sublattices and the corresponding phase transitions are concluded to be of the same kind. On the other hand, for even values of q the phase diagrams of the AF-AN_{q} models are different from the FM-N_{q} models and their topology does not change with q. Besides the pure AF and AN_{q} phases, observed at higher temperatures in the regions of the dominant respective couplings, at low temperatures there is a new canted (C)AF phase, which results from the competition between the AF and AN_{q} ordering tendencies and has no counterpart in the FM-N_{q} model. The phase transitions to the CAF phase from both AF and AN_{q} phases appear to be of the Berezinskii-Kosterlitz-Thouless nature.

Phase ordering, topological defects, and turbulence in the three-dimensional incompressible Toner-Tu equation

We investigate the phase-ordering dynamics of the incompressible Toner-Tu equation in three dimensions. We show that the phase ordering proceeds via defect merger events and the dynamics is controlled by the Reynolds number Re. At low Re, the dynamics is similar to that of the Ginzburg-Landau equation. At high Re, turbulence controls phase ordering. In particular, we observe a forward energy cascade from the coarsening length scale to the dissipation scale, clustering of defects, and multiscaling in velocity correlations.

Magnetic quasi-long-range ordering in nematic systems due to competition between higher-order couplings

Critical properties of the two-dimensional XY model involving solely nematic-like terms of the second and third orders are investigated by spin-wave analysis and Monte Carlo simulation. It is found that, even though neither of the nematic-like terms alone can induce magnetic ordering, their coexistence and competition leads to an extended phase of the magnetic quasi-long-range-order phase, wedged between the two nematic-like phases induced by the respective couplings. Thus, except for the multicritical point, at which all the phases meet, for any finite value of the coupling parameters ratio there are two phase transition: one from the paramagnetic phase to one of the two nematic-like phases followed by another one at lower temperatures to the magnetic phase. The finite-size scaling analysis indicates that the phase transitions between the magnetic and nematic-like phases belong to the Ising and three-state Potts universality classes. Inside the competition-induced algebraic magnetic phase, the spin-pair correlation function is found to decay even much more slowly than in the standard XY model with purely magnetic interactions. Such a magnetic phase is characterized by an extremely low vortex-antivortex pair density attaining a minimum close to the point at which the two couplings are of about equal strength.

XY model with higher-order exchange

An XY model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model displays a quasi-long-range-order phase characterized by an algebraically decaying correlation function with the exponent η=T/[2πJ(p,α)], nonlinearly dependent on the parameters p and α that control the number of the higher-order terms and the decay rate of their intensity, respectively. At higher temperatures the system shows a crossover from the continuous Berezinskii-Kosterlitz-Thouless to the first-order transition for the parameter values corresponding to a highly nonlinear shape of the potential well. The role of topological excitations (vortices) in changing the nature of the transition is discussed.

Quasi-Long-Range Order and Vortex Lattice in the Three-State Potts Model

We show that the order-disorder phase transition in the three-state Potts ferromagnet on a square lattice is driven by a coupled proliferation of domain walls and vortices. Raising the vortex core energy above a threshold value decouples the proliferation and splits the transition into two. The phase between the two transitions exhibits an emergent U(1) symmetry and quasi-long-range order. Lowering the core energy below a threshold value also splits the order-disorder transition but the system forms a vortex lattice in the intermediate phase.

Extending multiple histogram reweighting to a continuous lattice spin system exhibiting a first-order phase transition

We present extensive Monte Carlo simulations on a two-dimensional XY model with a modified form of interaction potential. Thermodynamic quantities other than energy, specific heat, etc. (such as magnetization, susceptibility, and fourth-order cumulant of magnetization) are obtained using multiple histogram reweighting of the data obtained from the simulations. We employ an approach which eliminates the need to construct two-dimensional histograms. This approach makes judicious use of computer memory as well as CPU time. Lee-Kosterlitz's method of finite size scaling for a first-order transition and analysis using Binder's cumulant method allow us to make an accurate determination of the transition temperature.

Nonuniversal behavior of the helicity modulus in a dense defect system

An extensive Monte Carlo simulation has been performed on a two-dimensional modified XY model that behaves like a dense defect system. Topological defects are shown to introduce disorder in the system, which makes the helicity modulus jump nonuniversal. The results corroborate the experimental observation of a nonuniversal jump of the superconducting density in high-Tc superconducting films.