## 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.

- Behavioral and Decision Sciences Program
- Biological Basis of Behavior Program
- Center for Italian Studies
- Cinema and Media Studies Program
- Classical Studies at Penn
- College of Arts and Sciences
- Department of Anthropology
- Department of Biology
- Department of Chemistry
- Department of Criminology
- Department of Earth and Environmental Science
- Department of East Asian Languages and Civilizations

## Search results

Publication Dilute Spin Glass at Zero Temperature in General Dimension(1989-09-01) Klein, Lior; Adler, Joan; Aharony, Amnon; Harris, A. Brooks; Meir, YigalWe 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, AmnonConnecting 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, YigalThe 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 Distribution of the Logarithms of Currents in Percolating Resistor Networks. I. Theory(1993-03-01) Aharony, Amnon; Blumenfeld, Raphael; Harris, A. BrooksThe 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 Series Analysis of Randomly Diluted Nonlinear Resistor Networks(1986-09-01) Meir, Yigal; Blumenfeld, Raphael; Aharony, Amnon; Harris, A. BrooksThe behavior of a randomly diluted network of nonlinear resistors, for each of which the voltage-current relationship is |V|=r|I|α, is studied with use of series expansions in the concentration p of conducting bonds on d-dimensional hypercubic lattices. The average nonlinear resistance 〈R〉 between pairs of sites separated by the percolation correlation length, scales as |p-pc|−ζ(α). The exponent ζ(α) was evaluated for 0<α<∞ and d=2, 3, 4, 5, and 6, found to decrease monotonically from the exponent describing the minimal length, at α=0, via that of the linear resistance, at α=1, to the exponent characterizing the singly connected bonds, ξ(∞)≡1. Our results agree with known results for α=0 and α=1, also with recent results for general α at d=6-ε dimensions. The second moment 〈R2〉 was found to diverge as 〈R⟩2 (for all α and d), indicating a scaling form for the probability distribution of R.Publication Magnetization Measurements of Antiferromagnetic Domains in Sr_{2}Cu_{3}O_{4}Cl_{2}(2001-03-15) Parks, Beth; Kastner, Marc A; Kim, Youngjune; Harris, A. Brooks; Chou, Fangcheng; Entin-Wohlman, Ora; Aharony, AmnonThe Cu3O4 layer in Sr2Cu3O4Cl2 is a variant of the square CuO2 lattice of the high-temperature superconductors, in which the center of every second plaquette contains an extra Cu2+ ion. Whereas the ordering of the spins in the ground-state and the spin-wave excitations of this frustrated spin system are both well understood, we find peculiar behavior resulting from antiferromagnetic domain walls. Pseudodipolar coupling between the two sets of Cu2+ ions results in a ferromagnetic moment, the direction of which reflects the direction of the antiferromagnetic staggered moment, allowing us to probe the antiferromagnetic domain structure. After an excursion to the high fields (>1 T), as the field is lowered, we observe the growth of domains with ferromagnetic moment perpendicular to the field. This gives rise to a finite domain wall susceptibility at small fields, which diverges near 100 K, indicating a phase transition. We also find that the shape of the sample influences the domain-wall behavior.Publication Resistance Fluctuations in Randomly Diluted Networks(1987-03-01) Blumenfeld, Raphael; Meir, Yigal; Aharony, Amnon; Harris, A. BrooksThe resistance R(x,x’) between two connected terminals in a randomly diluted resistor network is studied on a d-dimensional hypercubic lattice at the percolation threshold pc. When each individual resistor has a small random component of resistance, R(x,x’) becomes a random variable with an associated probability distribution, which contains information on the distribution of currents in the individual resistors. The noise measured between the terminals may be characterized by the cumulants Mq(x,x’) of R(x,x’). When averaged over configurations of clusters, M¯q(x,x’)~‖x-x’‖ψ̃(q). We construct low-concentration series for the generalized resistive susceptibility, χ(q), associated with M¯q, from which the critical exponents ψ̃(q) are obtained. We prove that ψ̃(q) is a convex monotonically decreasing function of q, which has the special values ψ̃(0)=DB, ψ̃(1)=ζ̃R, and ψ̃(∞)=1/ν. (DB is the fractal dimension of the backbone, ζ̃R is the usual scaling exponent for the average resistance, and ν is the correlation-length exponent.) Using the convexity property and the accepted values of these three exponents, we construct two approximant functions for ψ(q)=ψ̃(q)ν, both of which agree with the series results for all q>1 and with existing numerical simulations. These approximants enabled us to obtain explicit approximate forms for the multifractal functions α(q) and f(q) which, for a given q, characterize the scaling with size of the dominant value of the current and the number of bonds having this current. This scaling description fails for sufficiently large negative q, when the dominant (small) current decreases exponentially with size. In this case χ(q) diverges at a lower threshold p*(q), which vanishes as q→-∞.Publication Complex Magnetic Order in the Kagomé Staircase Compound Co_{3}V_{2}O_{8}(2006-07-25) Chen, Ying; Lynn, Jeffrey W; Huang, Qingzhen; Woodward, F. Matthew; Yildirim, Taner; Lawes, Gavin J; Ramirez, Arthur P; Rogado, Nyrissa S; Cava, Robert J; Aharony, Amnon; Entin-Wohlman, Ora; Harris, A. BrooksCo3V2O8 (CVO) has a different type of geometrically frustrated magnetic lattice, a kagomé staircase, where the full frustration of a conventional kagomé lattice is partially relieved. The crystal structure consists of two inequivalent (magnetic) Co sites, one-dimensional chains of Co(2) spine sites, linked by Co(1) cross-tie sites. Neutron powder diffraction has been used to solve the basic magnetic and crystal structures of this system, while polarized and unpolarized single crystal diffraction measurements have been used to reveal a rich variety of incommensurate phases, interspersed with lock-in transitions to commensurate phases. CVO initially orders magnetically at 11.3K into an incommensurate, transversely polarized, spin density wave state, with wave vector k=(0,δ,0) with δ=0.55 and the spin direction along the a axis. δ is found to decrease monotonically with decreasing temperature and then locks into a commensurate antiferromagnetic structure with δ=1/2 for 6.9Publication Ordering Due to Quantum Fluctuations in Sr_{2}Cu_{3}O_{4}Cl_{2}(1999-07-26) Kim, Youngjune; Aharony, Amnon; Birgeneau, Robert J; Chou, Fangcheng; Entin-Wohlman, Ora; Erwin, Ross W; Greven, Martin; Harris, A. Brooks; Kastner, Marc A; Korenblit, I. Ya; Lee, Youngsu; Shirane, GenSr2Cu3O4Cl2 has CuI and CuII subsystems, forming interpenetrating S=1/2 square lattice Heisenberg antiferromagnets. The classical ground state is degenerate, due to frustration of the intersubsystem interactions. Magnetic neutron scattering experiments show that quantum fluctuations cause a two dimensional Ising ordering of the CuII's, lifting the degeneracy, and a dramatic increase of the CuI out-of-plane spin-wave gap, unique for order out of disorder. The spin-wave energies are quantitatively predicted by calculations which include quantum fluctuations.Publication Diffusion on Percolating Clusters(1987-12-01) Harris, A. Brooks; Meir, Yigal; Aharony, AmnonThe moments τk of typical diffusion times for ‘‘blind’’ and ‘‘myopic’’ ants on an arbitrary cluster are expressed exactly in terms of resistive correlations for the associated resistor network. For a diluted lattice at bond concentration p, we introduce ‘‘diffusive’’ susceptibilities χk(p) as the average over clusters of τk. For p→pc, where pc is the percolation threshold, χk(p) diverges as |pc-p|-γk. We show that γk=kΔτ-β with Δτ=β+γ+ζ, where β and γ are percolation exponents and ζ is the resistance scaling exponent. Our analysis provides the first analytic demonstration that the leading exponents γk are the same for a wide class of models, including the two types of ants as special cases, although corrections to scaling are larger for the myopic ant than for the blind one. This class of models includes that for dilute spin waves in Heisenberg ferromagnets. Exact enumerations allow us to study universal amplitude ratios (at p=pc)χk+1χk−1/χk2 as a function of continuous spatial dimension d. For d>6 these ratios assume a constant value which for k=2 agrees with the exact result for the Cayley tree. The χk have the scaling properties predicted by Gefen, Aharony, and Alexander [Phys. Rev. Lett. 50, 77 (1983)] for anomalous diffusion.