Frustrated XY Model Research Articles

Zero-temperature transition and correlation-length exponent of the frustratedXYmodel on a honeycomb lattice

Phase coherence and vortex order in the fully frustrated XY model on a two-dimensional honeycomb lattice are studied by extensive Monte Carlo simulations using the parallel tempering method and finite-size scaling. No evidence is found for an equilibrium order-disorder or a spin/vortex-glass transition, suggested in previous simulation works. Instead, the scaling analysis of correlations of phase and vortex variables in the full equilibrated system is consistent with a phase transition where the critical temperature vanishes and the correlation lengths diverge as a power-law with decreasing temperatures and corresponding critical exponents $\nu_{ph}$ and $\nu_{v}$. This behavior and the near agreement of the critical exponents suggest a zero-temperature transition scenario where phase and vortex variables remain coupled on large length scales.

Finite-temperature phase structures of hard-core bosons in an optical lattice with an effective magnetic field

We study finite-temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to an effective magnetic field by employing the gauged CP$^1$ model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated XY model with only the phase as a dynamical variable. This suggests that cold atom simulators of the frustrated XY model are available irrespective of the particle filling at each site.

Critical behavior of the two-dimensional fully frustrated XY model

Critical behavior of the two-dimensional fully frustrated XY model has been investigated with Monte Carlo methods. Based on the dynamic scaling ansatz of the magnetization for temperatures above the transition temperature, the correlating time, spatial correlation length has been extracted. Fitting the correlation length to the exponential singularity assumed for the Kosterlitz–Thouless (KT) transition, the transition temperature TKT and the static exponent ν have been determined. The TKT = 0.45065(3) is one percent or two higher than that estimated from simulations in equilibrium. Moreover, the exponent ν = 0.089(2) is smaller than the theoretical value 0.5.

Spin-chirality decoupling and critical properties of a two-dimensional fully frustratedXYmodel

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.

Unified phase diagram for the three-dimensionalXYmodel of a point-disordered type-II superconductor

We carry out extensive Monte Carlo simulations of the three-dimensional uniformly frustrated XY model with uncorrelated randomly perturbed couplings, as a model for the equilibrium behavior of an e ...

Uniformly frustrated Josephson junction array in trapped Bose-Einstein condensates

We investigate the ground state structure of two-dimensional Josephson junction arrays consisting of Bose-Einstein condensates trapped by both a rotating harmonic potential and a corotating deep optical lattice with square symmetry. Monte Carlo simulations of the uniformly frustrated XY model in a wide range of the frustration parameter f reveal that the stable configuration of vortices for a simple fractional number f is a staircase structure, consisting of diagonal chains of vortices with periodic lattice of unit cells.

Dynamic Simulation of Kosterlitz–Thouless Transition in Two-Dimensional Fully Frustrated XY Model

Relaxation dynamics of the two-dimensional fully frustrated XY model is investigated with Monte Carlo methods. The simulation focuses on the Kosterlitz–Thouless phase transition. From the dynamic scaling behaviour of the magnetization above the transition temperature TKT, the correlating time of the dynamic system is extracted. The transition temperature TKT and static exponent v are then determined.

The dynamic exponent of two-dimensional fully frustrated XY model

With a large-scale Monte Carlo simulation, non-equilibrium dynamics of the two-dimensional fully frustrated XY model is investigated. We tackle the Kosterlitz-Thouless phase transition. Starting from an ordered initial state, we study the dynamic evolution of the magnetization as well as a specifically defined Binder cumulant. From the dynamic scaling ansatz, we extract the correlating time of the dynamics and the spatial correlation length of the equilibrium state. The dynamic exponent z is determined with relatively high accuracy. Especially, we suggest and demonstrate how one may directly measure the dynamic exponent z above TKT from the scaling fit of the Binder cumulant. These results indicate that the dynamic exponent z fluctuates around z=2, and this is consistent with that observed at temperatures below the transition temperature TKT.

Short-Time Dynamical Behaviour of Depinning Transition in the Uniformly Frustrated Two-Dimensional XY Model

A short-time dynamic scaling approach is extended to study the depinning transition of the two-dimensional frustrated XY model driven by external currents. We investigate the scaling behaviour of depinning transition in the XY model with three different flux densities f = 1/2, 1/25, 1/30. The short-time scaling behaviour in the depinning transition of the two-dimensional XY model is clearly shown up. Besides the critical current, the exponent θ is obtained.

The uniformly frustrated two-dimensional XY model in the limit of weak frustration

We consider the two-dimensional uniformly frustrated XY model in the limit of small frustration, which is equivalent to an XY system, for instance a Josephson junction array in a weak uniform magnetic field applied along a direction orthogonal to the lattice. We show that the uniform frustration (equivalently, the magnetic field) destabilizes the line of fixed points which characterize the critical behavior of the XY model for T ⩽ TKT, where TKT is the Kosterlitz–Thouless transition temperature: the system is paramagnetic at any temperature for sufficiently small frustration. We predict the critical behavior of the correlation length and of gauge-invariant magnetic susceptibilities as the frustration goes to zero. These predictions are fully confirmed by the numerical simulations.

Vortex Lattices in Rotating Bose-Einstein Condensate in an Optical Lattice: Analogy to Uniformly Frustrated Josephson-Junction Arrays

We investigate the effect of rotation for two-dimensional Josephson junction arrays consisting of atomic Bose-Einstein condensates trapped by both a harmonic trap and an optical lattice. This system is analogous to the superconducting Josephson junction array to which a transverse magnetic field is applied, being described by the uniformly frustrated XY model. The frustration parameter f, defined by the rotation frequency of the condensate and the lattice constant of the optical lattice, is an important parameter to determine the ground state. The numerical simulations of the Gross-Pitaevskii equation reveal that for f=1/2 the ground state possesses the checkerboard pattern of vortices, and for f<1/2 the vortex configuration is characterized by the staircase form.

Superconducting Transitions in Wire Network under Spatially Modulated Magnetic Field

Superconducting wire network subjected to a uniform and a checkerboard-patterned magnetic field is investigated. The checkerboard field is created by an array of ferromagnetic dots placed on top of the superconducting network. Measurements of the current–voltage ( I – V ) characteristics have revealed the canonical Kosterlitz–Thouless–Berezinskii (KTB) transition at zero magnetic field. The superconducting transition at α=1/2 (α being the frustration parameter) is studied in detail, and compared with the theoretical predictions on the fully frustrated XY model which has a double degeneracy in the ground state vortex configuration. The I – V characteristics for α=1/2 is consistent with the scenario of kink–antikink unbinding at antiphase domain boundaries first proposed by Korshunov [Phys. Rev. Lett. 88 (2002) 167007]. Introduction of the checkerboard field with amplitude β to the α=1/2 case lifts the double degeneracy. The effect of non-zero β on the nature of superconducting transition at α=1/2 is consis...

The melting transition of a vortex lattice in the uniformly frustratedXY model with quasi-one-dimensional and quasi-two-dimensional coupling anisotropy

The uniformly frustrated XY model on the cubic lattice with an anisotropic coupling constant is studied numerically.Quasi-one-dimensional and quasi-two-dimensional systems are examined as models for acharge density wave in a ring crystal and a layer superconductor, respectively. Themelting transition of a vortex lattice is investigated by means of non-equilibriumrelaxation analysis. We find scaling behaviour of the relaxation with a power law,which indicates that the phase transition is of second order, in contrast to thefirst-order transition in the isotropic case. The critical exponents are estimated asβ = 0.28 and zν = 2.3 for the quasi-one-dimensional system andβ = 0.40 and zν = 2.9 for the quasi-two-dimensional system, andα≈0 for both cases. This implies that the universality classes of the two are different.

Depinning of the Bragg Glass in a Point Disordered Model Superconductor

We perform simulations of the three-dimensional frustrated anisotropic XY model with point disorder as a model of a type-II superconductor with quenched point pinning in a magnetic field and a weak applied current. Using resistively shunted junction dynamics, we find a critical current I_{c} that separates a creep region with immeasurably low voltage from a region with a voltage V proportional, variant(I-I_{c}) and also identify the mechanism behind this behavior. It also turns out that data at fixed disorder strength may be collapsed by plotting V versus TI, where T is the temperature, though the reason for this behavior as yet not is fully understood.

Vortex Line Ordering in the Driven Three-Dimensional Vortex Glass

Resistively shunted junction dynamics is applied to the three-dimensional uniformly frustrated XY model with randomly perturbed couplings, as a model for driven steady states in a type-II superconductor with quenched point pinning. For a disorder strength p strong enough to produce a vortex glass in equilibrium, we map the phase diagram as a function of temperature T and uniform driving current I. Using finite size analysis and averaging over many realizations of quenched randomness we find a first-order melting T(m)(I) from a vortex line smectic to an anisotropic liquid.

Critical behavior of two-dimensional fully frustrated XY systems

We study the phase diagram of the two-dimensional fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present Monte Carlo simulations on square lattices L × L, L ≲ 103. We show that the low-temperature phase of these models is controlled by the same line of Gaussian fixed points as in the standard XY model. We find that, if a model undergoes a unique transition by varying temperature, then the transition is of first order. In the opposite case we observe two very close transitions: a transition associated with the spin degrees of freedom and, as temperature increases, a transition where chiral modes become critical. If they are continuous, they belong to the Kosterlitz-Thouless and to the Ising universality class, respectively. Ising and Kosterlitz-Thouless behavior is observed only after a preasymptotic regime, which is universal to some extent. In the chiral case, the approach is nonmonotonic for most observables, and there is a wide region in which finite-size scaling is controlled by an effective exponent νeff ≈ 0.8. This explains the result ν ≈ 0.8 of many previous studies using smaller lattices.

Vortex glass transitions in disordered three-dimensionalXYmodels: Simulations for several different sets of parameters

The anisotropic frustrated 3D XY model with strong disorder in the coupling constants is studied as a model of a disordered superconductor in an applied magnetic field. Simulations with the exchange Monte Carlo method are performed for frustrations f=1/5 and f=1/4, corresponding to two different values of the magnetic field along the z direction. The anisotropy is also varied. The determination of the helicity modulus from twist histograms is discussed in some detail and the helicity modulus is used in finite size scaling analyses of the vortex glass transition. The general picture is that the behavior in [Phys. Rev. Lett. 91, 077002 (2003)] is confirmed. For strong (e.g. isotropic) coupling in the z direction the helicity modulus fails to scale and it is argued that this is due to a too small effective randomness of such systems for the accessible system sizes.

Short-time dynamic behavior of two-dimensional fully frustrated XY model with time dependent Ginzburg–Landau dynamics

The Ising-like phase transition of two-dimensional fully frustrated XY (FFXY) model with time dependent Ginzburg–Landau (TDGL) dynamics is studied by using the short-time dynamics scaling analysis. The transition temperature T c and the dynamic and static critical exponents z, 2 β / ν , and ν are estimated and are compared with the results of FFXY model under resistively-shunted junction dynamics (RSJ) and Monte Carlo (MC) dynamics. We find T c , z, and ν are roughly independent of dynamic mode but 2 β / ν is dependent on the dynamic mode.

The [formula omitted] phase transition in the fully frustrated XY model as a percolation problem

The fully frustrated planar rotator and fully frustrated XY models in two dimensions have two phase transitions: one of the Berezinskii–Kosterlitz–Thouless type and other in the Ising universality class. We use Monte Carlo simulation to study both models. We fix our attention in the Ising-like transition, which we show can be understood as a percolation transition. We obtain the critical temperature as well as the critical exponents of the mean cluster size, γ , and Fisher's exponent τ . The critical temperature agree very well with other calculations. We found that the critical exponents are smaller than in the pure two-dimensional percolation case. We interpret this as due to the long-range interaction between vortex and antivortex.

Nonomura and Hu Reply:

We reply to a recent Comment on our previous article [Phys. Rev. Lett. 86, 5140 (2001)] by Olsson and Teitel [cond-mat/0404473]. We point out that their scaling argument to question the possible vortex slush phase in the frustrated XY model with point defects cannot be sufficiently justified by the provided numerical data, and that their data are indeed consistent with our previous article.