Stationary point approach to the phase transition of the classical XY chain with power-law interactions

The stationary points of the Hamiltonian H of the classical XY chain with power-law pair interactions (i.e., decaying like r^{-{\alpha}} with the distance) are analyzed. For a class of "spinwave-type" stationary points, the asymptotic behavior of the Hessian determinant of H is computed analytically in the limit of large system size. The computation is based on the Toeplitz property of the Hessian and makes use of a Szeg\"o-type theorem. The results serve to illustrate a recently discovered relation between phase transitions and the properties of stationary points of classical many-body Hamiltonian functions. In agreement with this relation, the exact phase transition energy of the model can be read off from the behavior of the Hessian determinant for exponents {\alpha} between zero and one. For {\alpha} between one and two, the phase transition is not manifest in the behavior of the determinant, and it might be necessary to consider larger classes of stationary points.Comment: 9 pages, 6 figure

On the interactions of lipids and proteins in the red blood cell membrane

The effects of temperature and of the action of a purified phospholipase C enzyme preparation on human red blood cell membranes has been investigated by chemical analyses, circular dichroism, and proton magnetic resonance measurements. The results indicate that a substantial fraction of the phospholipids and the proteins of the membranes can change structure independently of one another, suggesting a mosaic pattern for the organization of the lipids and proteins in membranes

Learning-Focused Leadership and Leadership Support: Meaning and Practice in Urban Systems

Synthesizes three reports on what good education leadership means and how it can best be supported, including the role of the school leader and the transformation of central district offices to focus more on improving instruction. Outlines key practices

Isotropic and Anisotropic Lattice Spacing Corrections for I=2 pi-pi Scattering from Effective Field Theory

The calculation of the finite lattice spacing corrections for I=2 pi-pi scattering is carried out for isotropic and anisotropic Wilson lattice actions. Pion masses and decay constants are also determined in this context. These results correct the phase shift calculated from the lattice, which is connected to the scattering length and effective range in this low energy scattering process. When in terms of the lattice-physical parameters for either Wilson action, these lattice spacing effects first appear at the next-to-leading order counter-terms.Comment: 15 pages, additional discussion of pion decay constant, version published in PR

Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium: Diagrams with Polarization Loops

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with electron and muon vacuum polarizations. We calculate single-logarithmic and nonlogarithmic contributions of order $\alpha^3(m/M)E_F$ generated by gauge invariant sets of diagrams with electron and muon polarization insertions in the electron and muon factors. Combining the new contributions with our older results we present complete result for all three-loop radiative-recoil corrections generated by the diagrams with electron and muon polarization loops.Comment: 8 pages, 10 figures. Editorial changes, results unchanged. Version published in Phys.Rev.Let