Dynamical scaling: the two-dimensional XY model following a quench

To sensitively test scaling in the two-dimensional XY model quenched from high temperatures into the ordered phase, we study the difference between measured correlations and the (scaling) results of a Gaussian-closure approximation. We also directly compare various length scales. All of our results are consistent with dynamical scaling and an asymptotic growth law L approximately (t/ln[t/t(0)])(1/2), though with a time scale t(0) that depends on the length scale in question. We then reconstruct correlations from the minimal-energy configuration consistent with the vortex positions, and find them significantly different from the "natural" correlations - though both scale with L. This indicates that both topological (vortex) and nontopological "spin-wave" contributions to correlations are relevant arbitrarily late after the quench. We also present a consistent definition of dynamical scaling applicable more generally, and emphasize how to generalize our approach to other quenched systems where dynamical scaling is in question. Our approach directly applies to planar liquid-crystal systems.     

Deconfinement in the two-dimensional XY model

The unbinding of vortex-antivortex pairs for the classical two-dimensional XY model in a magnetic field is studied. A single such pair is connected by a string of overturned spins, leading to linear confinement. We show that this system supports two phase transitions, one in which closed strings proliferate, and a second in which vortices unbind. The transitions are shown to be dual to one another, and are remarkably continuous. Possible consequences for a variety of systems are discussed.     

Dynamics of the anisotropic two-dimensional XY model

In this paper we study the dynamics of the two-dimensional XY model with single-ion anisotropy, and spin S = 1, in the large D phase, and low temperatures, using the bond operator formalism. The in-plane structure factor is a delta function. The out of plane shows a three peak structure, which merges in a single peak at the Brillouin zone boundary. We analyze also spin currents generated by a magnetic field gradient. The spin conductivity is calculated, at finite temperature, using the Kubo formula. The model shows unconventional ballistic spin transport at finite temperature. The computed spin conductivity exhibits a nonzero Drude weight at finite temperature. For ω< 2m, where m is the energy gap, the spin conductivity is described solely by the Drude weight. There is a regular contribution to the spin conductivity for ω> 2m, which persist in the zero temperature limit. The conductivity at the critical point, and for small frequencies, is (gμ_B)²/ħ times a universal scaling function of ħω/k_B T.     

Zero-temperature ordering in the two-dimensional quantum XY model

We have calculated the probability distribution for the staggered magnetization at T=0 for the 2D antiferromagnetic quantum XY model on finite lattices. For the ground state, the distribution shows evidence of isotropic magnetization ordering on the xy-plane. Based on data on seven lattices up to 26 sites, the extrapolated value of the staggered magnetization is 0.448±0.003 in the thermodynamic limit.     

Quantum phase transition in the two-dimensional XY model with single-ion anisotropy

In this paper we study the quantum phase transition and low temperature behavior in a square lattice quantum two-dimensional XY model with single-ion anisotropy and spin S=1. Starting with the Villain representation, a Landau-Ginzburg expression is written. The large D phase is studied using the bond operator formalism.     

Intrinsic finite-size effects in the two-dimensional XY model with irrational frustration

This study investigates in detail the finite-size scaling of the two-dimensional irrationally frustrated XY model. By means of Monte Carlo simulations with entropic sampling, we examine the size dependence of the specific heat, and find remarkable deviation from the conventional finite-size scaling theory, which reveals novel intrinsic finite-size effects. Relaxation dynamics of the system is also considered, and, correspondingly, finite-size scaling of the relaxation time is examined, again giving evidence for the intrinsic finite-size effects and suggesting a zero-temperature glass transition.     

Phase diagram for the two-dimensional quantum anisotropic XY model

A self-consistent harmonic approximation is used to study the Kosterlitz–Thouless phase transition and the quantum phase transition at T=0 K in the two-dimensional anisotropic quantum XY model.     

Dynamical phase transitions in the two-dimensional ANNNI model

We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly see several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.     

Thermodynamics of the two-dimensional spin-1/2 XY model

The generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto several three-dimensional Ising models with complicated many-spin interactions. This hierarchy of Ising-like models is studied by means of analytic and Monte Carlo techniques. We demonstrate that the sequence of these Ising models can be used to calculate accurately the thermodynamics of the two-dimensional spin-1/2 XY model. By calculating the specific heat, spin correlation functions, susceptibilities and a disorder parameter, we address the question of the nature of the phase transition in the two-dimensional spin-1/2 XY model.