Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice

We study the anti-ferromagnetic six-state clock model with nearest neighbor interactions on a triangular lattice with extensive Monte-Carlo simulations. We find clear indications of two phase transitions at two different temperatures: Below $T_I$ a chirality order sets in and by a thorough finite size scaling analysis of the specific heat and the chirality correlation length we show that this transition is in the Ising universality class (with a non-vanishing chirality order parameter below $T_I$). At $T_{KT}(<T_I)$ the spin-spin correlation length as well as the spin susceptibility diverges according to a Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below $T_{KT}$. We compare our results to recent x-ray diffraction experiments on the orientational ordering of CF$_3$Br monolayers physisorbed on graphite. We argue that the six-state clock model describes the universal feature of the phase transition in the experimental system and that the orientational ordering belongs to the KT universality class.Comment: 8 pages, 9 figure

Phase transitions in a frustrated XY model with zig-zag couplings

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 $\rho$ 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 behavior. Depending on the value of $\rho$, two separate transitions or a transition line in the universality class of the XY-Ising model, with combined $Z_2$ 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 ($Z_2$) 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 suggests 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.Comment: 11 pages, 9 figures, RevTex, to appear in Phys. Rev.

Thermal excitations of frustated XY spins in two dimensions

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 provides support for a single phase transition scenario in the FFTXY and FFSQXY models.Comment: 32 pages, RevTex, 11 eps figures available upon request, article to appear in Phys. Rev.

Enhancement of pair correlation in a one-dimensional hybridization model

We propose an integrable model of one-dimensional (1D) interacting electrons coupled with the local orbitals arrayed periodically in the chain. Since the local orbitals are introduced in a way that double occupation is forbidden, the model keeps the main feature of the periodic Anderson model with an interacting host. For the attractive interaction, it is found that the local orbitals enhance the effective mass of the Cooper-pair-like singlets and also the pair correlation in the ground state. However, the persistent current is depressed in this case. For the repulsive interaction case, the Hamiltonian is non-Hermitian but allows Cooper pair solutions with small momenta, which are induced by the hybridization between the extended state and the local orbitals.Comment: 11 page revtex, no figur

Cosmological distance indicators

We review three distance measurement techniques beyond the local universe: (1) gravitational lens time delays, (2) baryon acoustic oscillation (BAO), and (3) HI intensity mapping. We describe the principles and theory behind each method, the ingredients needed for measuring such distances, the current observational results, and future prospects. Time delays from strongly lensed quasars currently provide constraints on $H_0$ with < 4% uncertainty, and with 1% within reach from ongoing surveys and efforts. Recent exciting discoveries of strongly lensed supernovae hold great promise for time-delay cosmography. BAO features have been detected in redshift surveys up to z <~ 0.8 with galaxies and z ~ 2 with Ly-$\alpha$ forest, providing precise distance measurements and $H_0$ with < 2% uncertainty in flat $\Lambda$CDM. Future BAO surveys will probe the distance scale with percent-level precision. HI intensity mapping has great potential to map BAO distances at z ~ 0.8 and beyond with precisions of a few percent. The next years ahead will be exciting as various cosmological probes reach 1% uncertainty in determining $H_0$, to assess the current tension in $H_0$ measurements that could indicate new physics.Comment: Review article accepted for publication in Space Science Reviews (Springer), 45 pages, 10 figures. Chapter of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Ag

Propagating Disturbances in Coronal Loops: A Detailed Analysis of Propagation Speeds

Quasi-periodic disturbances have been observed in the outer solar atmosphere for many years now. Although first interpreted as upflows (Schrijver et al. (1999)), they have been widely regarded as slow magnetoacoustic waves, due to observed velocities and periods. However, recent observations have questioned this interpretation, as periodic disturbances in Doppler velocity, line width and profile asymmetry were found to be in phase with the intensity oscillations (De Pontieu et al. (2010),Tian1 et al. (2011))}, suggesting the disturbances could be quasi-periodic upflows. Here we conduct a detailed analysis of the velocities of these disturbances across several wavelengths using the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). We analysed 41 examples, including both sunspot and non sunspot regions of the Sun. We found that the velocities of propagating disturbances (PDs) located at sunspots are more likely to be temperature dependent, whereas the velocities of PDs at non sunspot locations do not show a clear temperature dependence. We also considered on what scale the underlying driver is affecting the properties of the PDs. Finally, we found that removing the contribution due to the cooler ions in the 193 A wavelength suggests that a substantial part of the 193 emission of sunspot PDs can be contributed to the cool component of 193\AA.Comment: 26 Papges, 15 Figure

Beach cleaning trials Pendine sands 1983

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