Department of Physics PapersCopyright (c) 2016 University of Pennsylvania All rights reserved.
http://repository.upenn.edu/physics_papers
Recent documents in Department of Physics Papersen-usFri, 01 Apr 2016 23:13:40 PDT3600Possible Orientationally Ordered States of Bucky-Cubane
http://repository.upenn.edu/physics_papers/488
http://repository.upenn.edu/physics_papers/488Fri, 21 Aug 2015 11:47:21 PDT
For temperatures above T^{∗ }= 130K C_{60}⋅C_{8}H_{8} forms a cubic crystal consisting of two interpenetrating fcc sublattices, one of freely rotating Buckys C_{60} and the other of orientationally ordered cubane C_{8}H_{8}. The crystal structure below a discontinuous transition is found to be orthorhombic, but the nature of the ordering of the Buckys has not yet been determined. Here possible orderings of the Buckys consistent with the size and symmetry of the orthorhombic unit cell are analyzed. Most likely inversion symmetry is preserved at the transition, in which case the small number of possible orderings are described. If inversion symmetry is removed, the point group can be C_{2v} which supports ferroelectricity or D_{2} which can be confirmed by proton NMR measurements.
]]>
A. Brooks HarrisPhonons and Their Coupling to Magnons in <em>n</em>=2 Ruddlesden-Popper Compounds
http://repository.upenn.edu/physics_papers/487
http://repository.upenn.edu/physics_papers/487Fri, 21 Aug 2015 11:40:37 PDT
The number of absorption and Raman optical modes for each Wyckoff orbit in the high-temperature tetragonal (I4/mmm) parent lattice of the Ruddlesden-Popper compounds Ca_{3}X_{2}O_{7}, with X=Mn or X=Ti is given. We analyze the effect of sequential perturbations which lower the symmetry to Cmcm and Cmc2_{1} and finally include magnetic ordering. We determine the power law behavior (within mean field theory) for the cross section for photon absorption and Raman scattering of modes which appear as the symmetry is successively lowered. In the Cmc2_{1} phase we give a symmetry analysis to discuss the magnon-phonon coupling which in other systems gives rise to "electromagnons." From our results we suggest several experiments to clarify the phase diagram and other properties of these systems.
]]>
A. Brooks HarrisMolecular Chirality and Chiral Parameter
http://repository.upenn.edu/physics_papers/486
http://repository.upenn.edu/physics_papers/486Fri, 21 Aug 2015 11:33:21 PDT
The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. The authors show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations but changing sign under improper rotations) and must involve three-point correlations that only come into play when the molecule has at least four atoms. In general, a molecule is characterized by an infinite set of chiral parameters. The authors illustrate the fact that these parameters can have differing signs and can vanish at different points as a molecule is continuously deformed into its mirror image. From this it is concluded that handedness is not an absolute concept but depends on the property being observed. Within a simplified model of classical interactions, the chiral parameter of the constituent molecules that determines the macroscopic pitch of cholesterics is identified.
]]>
A. Brooks Harris et al.Resistance of Random Walks
http://repository.upenn.edu/physics_papers/485
http://repository.upenn.edu/physics_papers/485Thu, 20 Aug 2015 08:46:22 PDT
Unrestricted lattice random walks in which a unit conductor is placed along each bond traversed are considered. The mean end-to-end resistance is studied as a function of the number of steps in the walk and the spatial dimension. A critical scaling law is found whose exponent is consistently given by four different calculational schemes.
]]>
Jayanth R. Banavar et al.ε Expansion for the Conductivity of a Random Resistor Network
http://repository.upenn.edu/physics_papers/484
http://repository.upenn.edu/physics_papers/484Thu, 20 Aug 2015 08:46:21 PDT
We present a reanalysis of the renormalization-group calculation to first order in ε=6−d, where d is the spatial dimensionality, of the exponent, t, which describes the behavior of the conductivity of a percolating network at the percolation threshold. If we set t=(d−2)ν_{p}+ζ, where ν_{p} is the correlation-length exponent, then our result is ζ=1+(ε/42). This result clarifies several previously paradoxical results concerning resistor networks and shows that the Alexander-Orbach relation breaks down at order ε.
]]>
A. Brooks Harris et al.Orientational Phases of Hydrogen Molecules on a Triangular Lattice
http://repository.upenn.edu/physics_papers/483
http://repository.upenn.edu/physics_papers/483Thu, 20 Aug 2015 08:46:19 PDT
A mean-field theory for the ordering of hydrogen molecules on a triangular net is derived in terms of the quadrupole coupling constant Γ, the crystal field V_{c}, and the temperature T. The phase diagram consists of six regions, separated by first- and second-order transitions. For almost all values of V_{c}/Γ for which ordering occurs, the disordered to ordered phase transition is continuous. At T=0 K, all phases have energy gaps except for a ferrorotational phase which behaves like an XY model.
]]>
A. John Berlinsky et al.1/z Expansion for the Heisenberg Antiferromagnet at Low Temperatures
http://repository.upenn.edu/physics_papers/482
http://repository.upenn.edu/physics_papers/482Thu, 20 Aug 2015 08:46:18 PDT
It is shown that the expansion in density of spin deviations for the Heisenberg antiferromagnet at low temperatures leads to a 1/z expansion for the free energy. In contrast to the 1/S expansion, the kinematic properties of spin operators are realized within each order of the expansion. The spin-wave energy at long wavelength is also calculated.
]]>
A. Brooks HarrisLocalization and Quantum Percolation
http://repository.upenn.edu/physics_papers/481
http://repository.upenn.edu/physics_papers/481Thu, 20 Aug 2015 08:46:17 PDT
Electronic wave functions are studied on dilute lattices, at dimensionalities 1⩽d⩽8. Generalized average inverse participation ratios are expanded in powers of the bond concentration, p. Dlog Padé approximants indicate that these ratios diverge as (p_{q}−p)^{-γq}, signaling the appearance of extended states for p>p_{q}. These Anderson transitions occur above classical percolation. No divergence is detected at d=2. These results are consistent with the existence of localized states at the center of the band.
]]>
Yonathan Shapir et al.Location of the Ising Spin-Glass Multicritical Point on Nishimori's Line
http://repository.upenn.edu/physics_papers/480
http://repository.upenn.edu/physics_papers/480Thu, 20 Aug 2015 08:46:16 PDT
We present arguments, based on local gauge invariance, that the multicritical point of Ising spin-glasses should be located on a particular line of the phase diagram known as Nishimori's line [tanh(βJ)=2p−1 for the ±J distribution]. One scaling axis is along the line, and the other is along the temperature direction. This scenario is generic for any random Ising model with a Nishimori line, in any number of dimensions, if the transitions are second order. The renormalization-group fixed point located inside Nishimori's manifold is expected to control multicriticality for a wider class of models.
]]>
Pierre Le Doussal et al.Comment on "Orientational Ordering Transition in Solid C<sub>60</sub>"
http://repository.upenn.edu/physics_papers/479
http://repository.upenn.edu/physics_papers/479Thu, 20 Aug 2015 08:46:15 PDT
A Comment on the Letter by P. A. Heiney et al., Phys. Rev. Lett. 66, 2911 (1991).
]]>
Ravi Sachidanandam et al.Vibrational Excitations in Percolation: Localization and Multifractality
http://repository.upenn.edu/physics_papers/478
http://repository.upenn.edu/physics_papers/478Thu, 20 Aug 2015 08:46:14 PDT
We discuss localized excitations on the incipient infinite percolation cluster. Assuming a simple exponential decay of the amplitudes ψ_{i} in terms of the chemical (minimal) path, we show theoretically that the ψ’s are characterized by a logarithmically broad distribution, and display multifractal features as a function of the Euclidean distance. The moments of ψ_{i} exhibit novel crossover phenomena. Our numerical simulations of fractons exhibit a nontrivial distribution of localization lengths, even when the chemical distance is fixed. These results are explained via a generalization of the theory.
]]>
Armin Bunde et al.Comment on "New Orientationally Ordered Low-Temperature Superstructure in High-Purity C<sub>60</sub>"
http://repository.upenn.edu/physics_papers/477
http://repository.upenn.edu/physics_papers/477Thu, 20 Aug 2015 08:46:12 PDT
A Comment on the Letter by G. Van Tendeloo et al. Phys. Rev. Lett. 69, 1065 (1992).
]]>
A. Brooks Harris et al.Was Superlocalization Observed in Carbon-Black–Polymer Composites?
http://repository.upenn.edu/physics_papers/476
http://repository.upenn.edu/physics_papers/476Thu, 20 Aug 2015 08:46:11 PDT
A Comment on the Letter by van der Putten, Phys. Rev. Lett. 69, 494 (1992).
]]>
Amnon Aharony et al.Evidence for Two Exponent Scaling in the Random Field Ising Model
http://repository.upenn.edu/physics_papers/475
http://repository.upenn.edu/physics_papers/475Thu, 20 Aug 2015 08:36:40 PDT
Novel methods were used to generate and analyze new 15 term high temperature series for both the (connected) susceptibility χ and the structure factor (disconnected susceptibility) χ_{d} for the random field Ising model with dimensionless coupling K=J/kT, in general dimension d. For both the bimodal and the Gaussian field distributions, with mean square field J^{2}g, we find that (χ_{d}-χ)/K^{2}gχ^{2}=1 as T→T_{c}(g), for a range of [h^{2}]=J^{2}g and d=3,4,5. This confirms the exponent relation γ^{¯}=2γ (where χ_{d}~t^{−γ¯}, χ~t^{−γ}, t=T-T_{c}) providing that random field exponents are determined by two (and not three) independent exponents. We also present new accurate values for γ.
]]>
Michael Gofman et al.Orientational Phase Transition in NaxC60 (1 < x < 3)
http://repository.upenn.edu/physics_papers/474
http://repository.upenn.edu/physics_papers/474Thu, 20 Aug 2015 08:36:38 PDT
X-ray diffraction and calorimetry data on cubic Na_{x}C_{60}(1<xT_{m} above that of pure C_{60}, e.g., T_{m}(x=1.3)=325 K. The ordered phases are the same as in pure C_{60}: simple cubic, space group Pa3^{¯}, but the orientations in the disordered phase are more restricted. We explain how Na stabilizes the ordered phase to rather high T, while K and Rb do not, in terms of Coulomb interactions between C_{60} molecules and and Na ions which we calculate from the local density approximation charge density of C_{60}.
]]>
Taner Yildirim et al.Spin Structures of Tetragonal Lamellar Copper Oxides
http://repository.upenn.edu/physics_papers/473
http://repository.upenn.edu/physics_papers/473Thu, 20 Aug 2015 08:36:37 PDT
The spin Hamiltonian of tetragonal lamellar antiferromagnets is shown to contain several novel anisotropies. Symmetry allows bond-dependent anisotropic exchange interactions, which lead to (a) interplane mean-field coupling and (b) an in-plane anisotropy which vanishes classically but arises from quantum zero point energy (QZPE). A similar QZPE involving the interplane isotropic interaction prefers collinear spins. Adding also diploar anisotropy, the competition between all these effects explains for the first time the spin structures of many cuprates.
]]>
Taner Yildirim et al.Symmetry, Spin-Orbit Interactions, and Spin Anisotropies
http://repository.upenn.edu/physics_papers/472
http://repository.upenn.edu/physics_papers/472Thu, 20 Aug 2015 08:36:35 PDT
The origins of anisotropy in the effective spin Hamiltonian, describing the ground manifold of Hubbard models with spin-orbit interactions, are critically discussed. For tetragonal symmetry, we show exactly that spin anisotropy can arise only if one includes both spin-orbit and Coulomb exchange interactions. For lower symmetries, additional anisotropies arise from terms which were hitherto neglected. Our analytic results are supported by numerical solutions for single bond clusters. These results can explain the easy plane anisotropy in the antiferromagnetic cuprates.
]]>
Taner Yildirim et al.Localization Length Exponent in Quantum Percolation
http://repository.upenn.edu/physics_papers/471
http://repository.upenn.edu/physics_papers/471Thu, 20 Aug 2015 08:36:34 PDT
Connecting perfect one-dimensional leads to sites i and j on the quantum percolation (QP) model, we calculate the transmission coefficient T_{ij}(E) at an energy E near the band center and the averages of Σ_{ij}T_{ij}, Σ_{ij}r^{2}_{ij}T_{ij}, and Σ_{ij}r^{4}_{ij}T_{ij}to tenth order in the concentration p. In three dimensions, all three series diverge at p_{q}=0.36^{+0.01}_{−0.02}, with exponents γ=0.82^{+0.10}_{−0.15}, γ+2ν, and γ+4ν. We find ν=0.38±0.07, differing from “usual” Anderson localization and violating the bound ν≥2/d of Chayes et al. [Phys. Rev. Lett. 57, 2999 (1986)]. Thus, QP belongs to a new universality class.
]]>
Iksoo Chang et al.Quantum Fluctuations in the Axial Next-Nearest-Neighbor Ising Model
http://repository.upenn.edu/physics_papers/470
http://repository.upenn.edu/physics_papers/470Thu, 20 Aug 2015 08:36:33 PDT
We obtain the axial next-nearest-neighbor Ising model from a Heisenberg model with large single-ion anisotropy energy, D, as might be relevant for helical spin systems. We treat quantum fluctuations to lowest order in 1/S at zero temperature within an expansion in J/D, where J is an exchange energy. The transition from the state with periodicity p=4 to the uniform state (p=∞) occurs via a sequence of first order transitions in which p increases monotonically.
]]>
A. Brooks Harris et al.Yildirim <em>et al.</em> Reply
http://repository.upenn.edu/physics_papers/469
http://repository.upenn.edu/physics_papers/469Thu, 20 Aug 2015 08:36:31 PDT
A Reply to the Comment by S. Skanthakumar, J. W. Lynn, and I. W. Sumarlin, Phys. Rev. Lett. 74, 2842 (1995).
]]>
Taner Yildirim et al.