[en] We study a new generalized version of the square-lattice frustrated XY model where unequal ferromagnetic and antiferromagnetic couplings are arranged in a zig-zag pattern. The ratio between the couplings ρ can be used to tune the system, continuously, from the isotropic square-lattice to the triangular-lattice frustrated XY model. The model can be physically realized as a Josephson-junction array with two different couplings, in a magnetic field corresponding to half-flux quanta per plaquette. Mean-field approximation, Ginzburg-Landau expansion and finite-size scaling of Monte Carlo simulations are used to study the phase diagram and critical behaviour. Depending on the value of ρ, two separate transitions or a transition line in the universality class of the XY-Ising model, with combined Z₂ and U(1) symmetries, takes place. In particular, the phase transitions of the standard square-lattice and triangular-lattice frustrated XY models correspond to two different cuts through the same transition line. Estimates of the chiral (Z₂) critical exponents on this transition line deviate significantly from the pure Ising values, consistent with that along the critical line of the XY-Ising model. This suggest that a frustrated XY model or Josephson-junction array with a zig-zag coupling modulation can provide a physical realization of the XY-Ising model critical line. (author). 32 refs, 9 figs

[en] We consider a Bose-Einstein condensate (BEC) of N atoms of repulsive interaction ∼ U₀, in an elliptical trap, axially pierced by a Gaussian-intensity laser beam, forming an effective (quasi-2D) toroidal trap with minimum at radial distance ρ = ρ_p. The macroscopic angular momentum states Ψ_l(ρ,θ) ∼ √NΦ_l(ρ)e^ilθ for integer l spread up to ρ < or approx. ρ_max ∼ (NU₀)^1/4 >> ρ_p. The spreading lowers rotational energies, so estimated low metastability barriers can support large l < or approx. l_max ∼ (NU₀)^1/4, < or approx. 10 for typical parameters. The l-dependent density profile module Φ_l(ρ)² -Φ₀(ρ)² is a signature of BEC rotation. Results are insensitive to off-axis laser displacements ρ₀, for ρ₀ ρ_max << 1. (author)

[en] We present a new variational approach to the study of phase transitions in frustrated 2D XY models. In the spirit of Villain's approach for the ferromagnetic case we divide thermal excitations into a low temperature long wavelength part (LW) and a high temperature short wavelength part (SW). In the present work we mainly deal with LW excitations and we explicitly consider the cases of the fully frustrated triangular (FFTXY) and square (FFSQXY) XY models. The novel aspect of our method is that it preserves the coupling between phase (spin angles) and chiral degrees of freedom. LW fluctuations consist of coupled phase and chiral excitations. As a result, we find that for frustrated systems the effective interactions between phase variables is long range and oscillatory in contrast to the unfrustrated problem. Using Monte Carlo (MC) simulations we show that our analytical calculations produce accurate results at all temperature T; this is seen at low T in the spin wave stiffness constant and in the staggered chirality; this is also the case near T_c: transitions are driven by the SW part associated with domain walls and vortices, but the coupling between phase and chiral variables is still relevant in the critical region. In that regime our analytical results yield the correct T dependence for bare couplings (given by the LW fluctuations) such as the Coulomb gas temperature T_CG of the frustrated XY models. In particular, we find that T_CG tracks chiral rather than phase fluctuations. Our results provide support for a single phase transition scenario in the FFTXY and FFSQXY models. (author). 35 refs, 8 figs

[en] It has recently become possible to synthesize a class of nanostructured materials by ion implantation. The implanted ions aggregate into crystallographically oriented nanoscale inclusions in the host material. We have performed simulations of the magnetization curves for such assemblies of nanoscale Fe inclusions in a nonmagnetic host. We use random positions for the magnetic particles (not a regular grid) and include magnetostatic interactions in detail. We find that these materials are not adequately described by standard noninteracting theories-interactions have a significant effect. In particular, interactions can mask the effects of crystallite orientation, producing nearly isotropic hysteresis curves. The use of a noninteracting model could thus lead one to conclude, incorrectly, that the inclusions are randomly oriented. [copyright] 2001 American Institute of Physics

[en] The row model for frustrated XY spins on a triangular lattice in 2D is used to study incommensurate (IC) and commensurate (C) phases, in the regime where a (C)-(IC) transition may be observed. Thermodynamic quantities for the (IC) state are computed analytically by means of the NSCHA, a new variational method appropriate for frustrated systems. On the commensurate side of the (C)-(IC) boundary, NSCHA predicts an instability of the (C) phase suggesting that this state is in fact spatially inhomogeneous. Detailed Monte-Carlo (MC) simulations using fluctuating boundary conditions and specific histogram techniques show that in this regime the configuration consists of stripes of (C) and (IC) phases alternating in space. This state, which resembles the smectic-A phase of liquid crystals, exists because of the strong coupling between chiral and phase (spin angle) variables. As a result, the transition between the (IC) and the (C) states can only occur at zero temperature T so that the Lifshitz point is at T = 0 for modulated XY spins in 2D. (author)

[en] Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical properties: it combines fluctuating boundary conditions and specific histogram techniques. Our approach concerns classical as well as quantum systems. In particular, current-current correlation functions, which probe large scale coherence of the states, can be accurately evaluated. We illustrate our method on a frustrated two dimensional XY model. (author)

[en] The effects of random dilution of junctions on a two-dimensional Josephson-junction array in a magnetic field are considered. For rational values of the average flux quantum per plaquette f, the superconducting transition temperature vanishes, for increasing dilution at a critical value xs(f), while the vortex ordering remains stable up to x_VL > X_S, much below the value x_p corresponding to the geometric percolation threshold. For x_VL < x < x_p, the array behaves as a zero-temperature vortex-glass. Numerical results for f = 1/2 from defect energy calculations are presented which are consistent with this scenario. (author)

[en] We study the stability of a rotating repulsive-atom Bose-Einstein condensate in a toroidal trap. The resulting macroscopic angular-momentum states with integer vorticity l spread radially, lowering rotational energies. These states are robust against vorticity-lowering decays, with estimated metastability barriers capable of sustaining large angular momenta (1 < or ∼ 10) for typical parameters. We identify the centrifugally squashed l-dependent density profile as a possible signature of condensate rotation and superfluidity. (author)