Penn Arts & Sciences

The University of Pennsylvania School of Arts and Sciences forms the foundation of the scholarly excellence that has established Penn as one of the world's leading research universities. We teach students across all 12 Penn schools, and our academic departments span the reach from anthropology and biology to sociology and South Asian studies.

Members of the Penn Arts & Sciences faculty are leaders in creating new knowledge in their disciplines and are engaged in nearly every area of interdisciplinary innovation. They are regularly recognized with academia's highest honors, including membership in prestigious societies like the National Academy of Sciences, the American Association for the Advancement of Science, the American Academy of Arts and Sciences, and the American Philosophical Society, as well as significant prizes such as MacArthur and Guggenheim Fellowships.

The educational experience offered by Penn Arts & Sciences is likewise recognized for its excellence. The School's three educational divisions fulfill different missions, united by a broader commitment to providing our students with an unrivaled education in the liberal arts. The College of Arts and Sciences is the academic home of the majority of Penn undergraduates and provides 60 percent of the courses taken by students in Penn's undergraduate professional schools. The Graduate Division offers doctoral training to over 1,300 candidates in more than 30 graduate programs. And the College of Liberal and Professional Studies provides a range of educational opportunities for lifelong learners and working professionals.


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Now showing 1 - 10 of 211
  • Publication
    Dilute Spin Glass at Zero Temperature in General Dimension
    (1989-09-01) Klein, Lior; Adler, Joan; Aharony, Amnon; Harris, A. Brooks; Meir, Yigal
    We study the zero-temperature critical behavior of the dilute Ising spin glass. In our model nearest-neighbor exchange interactions randomly assume the values +J, 0, -J with probabilities p/2, 1-p, and p/2, respectively. We have generated 15th-order series for the Edwards-Anderson spin-glass susceptibility as a function of concentration p on hypercubic lattices in general dimension. Their analysis leads to critical concentrations and exponents that differ from those of percolation.
  • Publication
    Localization Length Exponent in Quantum Percolation
    (1995-03-13) Chang, Iksoo; Lev, Zvi; Harris, A. Brooks; Adler, Joan; Aharony, Amnon
    Connecting perfect one-dimensional leads to sites i and j on the quantum percolation (QP) model, we calculate the transmission coefficient Tij(E) at an energy E near the band center and the averages of ΣijTij, Σijr2ijTij, and Σijr4ijTij to tenth order in the concentration p. In three dimensions, all three series diverge at pq=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.
  • Publication
    Dilute Random-Field Ising Models and Uniform-Field Antiferromagnets
    (1985-09-01) Aharony, Amnon; Harris, A. Brooks; Meir, Yigal
    The order-parameter susceptibility χ of dilute Ising models with random fields and dilute antiferromagnets in a uniform field are studied for low temperatures and fields with use of low-concentration expansions, scaling theories, and exact solutions on the Cayley tree to elucidate the behavior near the percolation threshold at concentration pc. On the Cayley tree, as well as for d>6, both models have a zero-temperature susceptibility which diverges as |ln(pc-p)|. For spatial dimensions 1< dpc- p)−(γp−βp)/2, where γp and βp are percolation exponents associated with the susceptibility and order parameter. At d=6, the susceptibilities diverge as |ln(pc-p)|9/7. For d=1, exact results show that the two models have different critical exponents at the percolation threshold. The (finite-length) series at d=2 seems to exhibit different critical exponents for the two models. At p=pc, the susceptibilities diverge in the limit of zero field h as χ~h-(γp-βp)/(γp+βp) for d9/7 for d=6, and as χ~|lnh| for d>6.
  • Publication
    Spin-Wave Spectra of Yttrium and Gadolinium Iron Garnet
    (1963-12-15) Harris, A. Brooks
    The problem of deducing the values of the exchange integrals in yttrium and gadolinium iron garnet from measurements of the magnetization and the magnetic contribution to the specific heat at low temperatures is considered. For these garnets the spin-wave normal modes can be found by solving the semiclassical equations of motion which give rise to a set of n simultaneous linear equations, where n is the number of magnetically inequivalent ions in the unit cell. Expressions for the thermodynamic functions at low temperatures in terms of the frequencies of the normal modes are given assuming the validity of the spin-wave approximation. It is argued that the temperature variation of the frequency of these normal modes on the macroscopic properties can be completely accounted for without considering the zero point energy explicitly. Due to the size of the unit cell, the equations for the frequencies of the normal modes can only be solved numerically for general values of k. Such solutions are obtained for k lying along a [111] direction for various values of the exchange integrals, and the thermodynamic functions corresponding to these choices of parameters are calculated. In the case of yttrium iron garnet, the value of D, the coefficient of a2k2 in the acoustic dispersion law, is reliably known and fixes one linear combination of Jaa, Jad, and Jdd. By comparing our calculations with the magnetization data of Solt, it was established that Jaa/Jad=0.2, but since the magnetization was not very sensitive to variations of the ratio Jdd/Jad its value could not be estimated precisely. Taking Jdd/Jad=0.2 gives Jaa=Jdd=6.35 cm−1 and Jad=31.8 cm−1. For GdIG the specific heat data below 20°K is not very much influenced by the exact values of the iron-iron exchange integrals which were taken to be those quoted above for yttrium iron garnet. Again one combination of Jac and Jdc is known from the calorimetric determination of the single ion splitting. By comparing the specific heat data below 5°K with calculations for various values of Jac/Jdc it was possible to determine Jac and Jdc separately: Jdc=7.00 cm−1 and Jac=1.75 cm−1. These values are about 25% larger than what one would expect using the Weiss molecular field approximation.
  • Publication
    Distribution of the Logarithms of Currents in Percolating Resistor Networks. I. Theory
    (1993-03-01) Aharony, Amnon; Blumenfeld, Raphael; Harris, A. Brooks
    The distribution of currents, ib, in the bonds b of a randomly diluted resistor network at the percolation threshold is investigated through a study of the moments of the distribution P^(i2) and the moments of the distribution P(y), where y=-lnib2. For q>qc the qth moment of P^(i2), Mq (i.e., the average of i2q), scales as a power law of the system size L, with a multifractal (noise) exponent ψ̃(q)-ψ̃(0). Numerical data indicate that qc is negative, but becomes small for large L. Assuming that all derivatives ψ̃(q) exist at q=0+, we show that for positive integer k the kth moment, μk, of P(y) is given by μk=(α0 lnL)k{1+[kC1+1/2k(k-1)D1] (lnL)−1+O[(lnL)−2]}, where α0 and D1 (but not C1) are universal constants obtained from ψ̃(q). A second independent argument, requiring an assumed analyticity property of the asymptotic multifractal function, f(α), leads to the same equation for all k. This latter argument allows us to include finite-size corrections to f(α), which are of order (lnL)−1. These corrections must be taken into account in interpreting numerical studies of P(y). We note that data for P(-lni2) seem to show power-law behavior as a function of i2 for small i. Values of the exponents are directly related to the values of qc, and the numerical data in two dimensions indicate it to be small (but probably nonzero). We suggest, in view of the nature of the finite-size corrections in the expression for μk, that the asymptotic regime may not have been reached in the numerical work. For d=6 we find that Mq(L)~(lnL)θ(q), where θ(q)→∞ for q→qc=-1/2.
  • Publication
    Symmetry Analysis of Multiferroic Co3TeO6
    (2012-03-12) Harris, A. Brooks
    A phenomenological explanation of the magnetoelectric behavior of Co3TeO6 is developed. We explain the second harmonic generation data and the magnetic field induced spontaneous electric polarization in the magnetically ordered phase below 20 K.
  • Publication
    Landau Analysis of the Symmetry of the Magnetic Structure and Magnetoelectric Interaction in Multiferroics
    (2007-08-28) Harris, A. Brooks
    This paper presents a detailed instruction manual for constructing the Landau expansion for magnetoelectric coupling in incommensurate ferroelectric magnets, including Ni3V2O8, TbMnO3, MnWO4, TbMn2O5, YMn2O5, CuFeO2, and RbFe(MO4)2. The first step is to describe the magnetic ordering in terms of symmetry adapted coordinates which serve as complex-valued magnetic order parameters whose transformation properties are displayed. In so doing, we use the previously proposed technique to exploit inversion symmetry, since this symmetry has seemingly been universally overlooked. Inversion symmetry severely reduces the number of fitting parameters needed to describe the spin structure, usually by fixing the relative phases of the complex fitting parameters. By introducing order parameters of known symmetry to describe the magnetic ordering, we are able to construct the trilinear magnetoelectric interaction which couples incommensurate magnetic order to the uniform polarization, and thereby we treat many of the multiferroic systems so far investigated. In most cases, the symmetry of the magnetoelectric interaction determines the direction of the magnetically induced spontaneous polarization. We use the Landau description of the magnetoelectric phase transition to discuss the qualitative behavior of various susceptibilities near the phase transition. The consequences of symmetry for optical properties such as polarization induced mixing of Raman and infrared phonons and electromagnons are analyzed. The implication of this theory for microscopic models is discussed.
  • Publication
    Spin Dynamics of Trimers on a Distorted Kagome Lattice
    (2013-07-11) Harris, A. Brooks; Yildirim, Taner
    We treat the ground state, elementary excitations, and neutron scattering cross section for a system of trimers consisting of three tightly bound spins 1/2 on a distorted kagome lattice, subject to isotropic nearest-neighbor (usually antiferromagnetic) Heisenberg interactions. The interactions between trimers are assumed to be weak compared to the intratrimer interactions. We compare the spin-wave excitation spectrum of trimers with that obtained from standard spin-wave theory and attribute the differences at low energy to the fact that the trimer formulation includes exactly the effects of intratrimer zero-point motion.
  • Publication
    Comment on "Ferroelectricity in Spiral Magnets"
    (2008-02-29) Kenzelmann, Michel; Harris, A. Brooks
    A Comment on the Letter by Maxim Mostovoy, [Phys. Rev. Lett. 96, 067601 (2006)]. The author of the Letter offers a Reply.
  • Publication
    Lattice Dynamics of Solid C60
    (1992-09-15) Yildirim, Taner; Harris, A. Brooks
    The lattice dynamics of C60 has been studied first by means of group theory and then by diagonalizing the dynamical matrix for two recently proposed intermolecular potentials. The libron and phonon energies are calculated as a function of momentum along various symmetry directions with and without phonon–libron interactions. The effects of these interactions on the density of states are also discussed. Explicit expressions for the energies of these modes at zero wave vector are given. It is found that both potential models have nearly the same phonon but a somewhat different libron spectrum. The calculated libron energies agree reasonably well with currently available experimental results.