Two-body correlations and the superfluid fraction for nonuniform systems

We extend the one-body phase function upper bound on the superfluid fraction in a periodic solid (a spatially ordered supersolid) to include two-body phase correlations. The one-body current density is no longer proportional to the gradient of the one-body phase times the one-body density, but rather it depends also on two-body correlation functions. The equations that simultaneously determine the one-body and two-body phase functions require a knowledge of one-, two-, and three-body correlation functions. The approach can also be extended to disordered solids. Fluids, with two-body densities and two-body phase functions that are translationally invariant, cannot take advantage of this additional degree of freedom to lower their energy.Comment: 13 page

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.

Magnetic field effects on the helical instability of the î //Vs texture in 3He-a

We have studied the effect of a magnetic field H, in the dipole-locked regime, on the stability of the î// Vs texture in 3He-A. An H 〉 Vs (H // Vs) tends to stabilize (destabilize) this texture.Nous étudions l'effet du champ magnétique H, dans le domaine où l'énergie dipolaire est prépondérante, sur la stabilité de la texture avec î//V s, dans 3He-A. Pour H 〉 Vs (resp. H// Vs) cette texture peut être stabilisée (resp. déstabilisée)