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We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length ξ, the susceptibility at the ordering wavevector χ(Q), and the spin stiffness ρ clearly reflects the existence of two temperature regimes -a high temperature regime T > T th , in which the disordering effect of vortices is dominant, and a low temperature regime T < T th , where correlations are controlled by small amplitude spin fluctuations. As has previously been shown, in the last regime, the behavior of the above quantities agrees well with the predictions of a renormalization group treatment of the appropriate nonlinear sigma model. For T > T th , a satisfactory fit of the data is achieved, if the temperature dependence of ξ and χ(Q) is assumed to be of the form predicted by the Kosterlitz-Thouless theory. Surprisingly, the crossover between the two regimes appears to happen in a very narrow temperature interval around T th ≃ 0.28.

We study the properties of the Heisenberg antiferromagnet with spatially anisotropic nearest-neighbor exchange couplings on the kagomé net, i.e., with coupling J in one lattice direction and couplings JЈ along the other two directions. For J / JЈ տ 1, this model is believed to describe the magnetic properties of the mineral volborthite. In the classical limit, it exhibits two kinds of ground state: a ferrimagnetic state for J / JЈ Ͻ 1/2 and a large manifold of canted spin states for J / JЈ Ͼ 1 / 2. To include quantum effects self-consistently, we investigate the Sp͑N͒ symmetric generalization of the original SU͑2͒ symmetric model in the large-N limit. In addition to the dependence on the anisotropy, the Sp͑N͒ symmetric model depends on a parameter that measures the importance of quantum effects. Our numerical calculations reveal that, in the -J / JЈ plane, the system shows a rich phase diagram containing a ferrimagnetic phase, an incommensurate phase, and a decoupled chain phase, the latter two with short-and long-range order. We corroborate these results by showing that the boundaries between the various phases and several other features of the Sp͑N͒ phase diagram can be determined by analytical calculations. Finally, the application of a block-spin perturbation expansion to the trimerized version of the original spin-1 / 2 model leads us to suggest that in the limit of strong anisotropy, J / JЈ ӷ 1, the ground state of the original model is a collinearly ordered antiferromagnet, which is separated from the incommensurate state by a quantum phase transition.

We study interacting electrons in two dimensions moving in the lowest Landau level under the condition that the Zeeman energy is much smaller than the Coulomb energy and the filling factor is one. In this case, Skyrmion quasiparticles play an important role. Here, we present a simple and transparent derivation of the corresponding effective Lagrangian. In its kinetic part, we find a nonzero Hopf term, the prefactor of which we determine rigorously. In the Hamiltonian part, we calculate, by means of a gradient expansion, the Skyrmion-Skyrmion interaction completely up to fourth order in spatial derivatives. [S0031-9007(97)02620-3] PACS numbers: 73.20.Dx, 71.35.Ji, 73.20.Mf, 75.30.Et Two-dimensional electron gases, as manufactured in GaAs heterostructures, show a rich variety of features as the strength of a magnetic field or the particle density is varied. Most prominent among these are the quantum Hall effects (QHEs) at integer and fractional filling factors n (n N e ͞N F , where N e and N F are the number of electrons and the orbital degeneracy of the Landau level, respectively). The existence of a well-defined single-particle spectrum of discrete, spin-split Landau levels allows one to explain the integer QHE. Until recently it was accepted that when in such a system the characteristic Coulomb energy is less than the cyclotron energy, the ordinary low-lying excitations are electron-hole pairs of opposite spins (spin excitons [1,2]). These have a nonzero kinetic energy with a strong k dispersion due to the electron-electron interaction. In a completely filled Landau level, the energy gap for creating a widely separated quasielectron-quasihole pair, a large spin exciton (i.e., one with k !`), is apart from the Zeeman splitting governed by the exchange energy associated with a hole, and is equal to jgjm B B 1 q p 2 e 2 kl H . Here, g is the effective single particle Landé factor and l H ͑ch͞eB͒ 1͞2 is the magnetic length. This is in qualitative agreement with experiments on the temperature-dependent longitudinal resistance in the thermally activated regime [3,4].Recent theoretical investigations [5,6] near filling factor n 1, however, revealed that the interplay between Zeeman and Coulomb interaction results in a more complex type of excitations with unusual spin order which can be described as Skyrmions. It was shown [5] that the energy gap required to create a widely separated Skyrmion-anti-Skyrmion pair, is only half of the gap required to create a large spin exciton. Skyrmions appeared originally in condensed matter physics in the context of the Heisenberg ferromagnet as solutions of the O͑3͒ nonlinear sigma model in two dimensions for nonzero values of the topological charge [7]. Provided now that the Zeeman energy is less than the Coulomb energy, the elec-tron gas is equivalent to an isotropic itinerant ferromagnet. The latter can then be described by a three-component order parameter in a 2D coordinate space, i.e., just by the O͑3͒ nonlinear sigma model [7][8][9] in which one finds topologically nontrivi...

The electronic states of an electrostatically confined cylindrical graphene quantum dot and the electric transport through this device are studied theoretically within the continuum Dirac-equation approximation and compared with numerical results obtained from a tight-binding lattice description. A spectral gap, which may originate from strain effects, additional adsorbed atoms or substrateinduced sublattice-symmetry breaking, allows for bound and scattering states. As long as the diameter of the dot is much larger than the lattice constant, the results of the continuum and the lattice model are in very good agreement. We also investigate the influence of a sloping dot-potential step, of on-site disorder along the sample edges, of uncorrelated short-range disorder potentials in the bulk, and of random magnetic-fluxes that mimic ripple-disorder. The quantum dot's spectral and transport properties depend crucially on the specific type of disorder. In general, the peaks in the density of bound states are broadened but remain sharp only in the case of edge disorder.