3,889 research outputs found

    Kertesz on Fat Graphs?

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    The identification of phase transition points, beta_c, with the percolation thresholds of suitably defined clusters of spins has proved immensely fruitful in many areas of statistical mechanics. Some time ago Kertesz suggested that such percolation thresholds for models defined in field might also have measurable physical consequences for regions of the phase diagram below beta_c, giving rise to a ``Kertesz line'' running between beta_c and the bond percolation threshold, beta_p, in the M, beta plane. Although no thermodynamic singularities were associated with this line it could still be divined by looking for a change in the behaviour of high-field series for quantities such as the free energy or magnetisation. Adler and Stauffer did precisely this with some pre-existing series for the regular square lattice and simple cubic lattice Ising models and did, indeed, find evidence for such a change in high-field series around beta_p. Since there is a general dearth of high-field series there has been no other work along these lines. In this paper we use the solution of the Ising model in field on planar random graphs by Boulatov and Kazakov to carry out a similar exercise for the Ising model on random graphs (i.e. coupled to 2D quantum gravity). We generate a high-field series for the Ising model on Φ4\Phi^4 random graphs and examine its behaviour for evidence of a Kertesz line

    The effects of space radiation on a chemically modified graphite-epoxy composite material

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    The effects of the space environment on the engineering properties and chemistry of a chemically modified T300/934 graphite-epoxy composite system are characterized. The material was subjected to 1.0 x 10 to the 10th power rads of 1.0 MeV electron irradiation under vacuum to simulate 30 years in geosynchronous earth orbit. Monotonic tension tests were performed at room temperature (75 F/24 C) and elevated temperature (250 F/121 C) on 4-ply unidirectional laminates. From these tests, inplane engineering and strength properties (E sub 1, E sub 2, Nu sub 12, G sub 12, X sub T, Y sub T) were determined. Cyclic tests were also performed to characterize energy dissipation changes due to irradiation and elevated temperature. Large diameter graphite fibers were tested to determine the effects of radiation on their stiffness and strength. No significant changes were observed. Dynamic-mechanical analysis demonstrated that the glass transition temperature was reduced by 50 F(28 C) after irradiation. Thermomechanical analysis showed the occurrence of volatile products generated upon heating of the irradiated material. The chemical modification of the epoxy did not aid in producing a material which was more radiation resistant than the standard T300/934 graphite-epoxy system. Irradiation was found to cause crosslinking and chain scission in the polymer. The latter produced low molecular weight products which plasticize the material at elevated temperatures and cause apparent material stiffening at low stresses at room temperature

    Complex-Temperature Singularities in the d=2d=2 Ising Model. III. Honeycomb Lattice

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    We study complex-temperature properties of the uniform and staggered susceptibilities χ\chi and χ(a)\chi^{(a)} of the Ising model on the honeycomb lattice. From an analysis of low-temperature series expansions, we find evidence that χ\chi and χ(a)\chi^{(a)} both have divergent singularities at the point z=1zz=-1 \equiv z_{\ell} (where z=e2Kz=e^{-2K}), with exponents γ=γ,a=5/2\gamma_{\ell}'= \gamma_{\ell,a}'=5/2. The critical amplitudes at this singularity are calculated. Using exact results, we extract the behaviour of the magnetisation MM and specific heat CC at complex-temperature singularities. We find that, in addition to its zero at the physical critical point, MM diverges at z=1z=-1 with exponent β=1/4\beta_{\ell}=-1/4, vanishes continuously at z=±iz=\pm i with exponent βs=3/8\beta_s=3/8, and vanishes discontinuously elsewhere along the boundary of the complex-temperature ferromagnetic phase. CC diverges at z=1z=-1 with exponent α=2\alpha_{\ell}'=2 and at v=±i/3v=\pm i/\sqrt{3} (where v=tanhKv = \tanh K) with exponent αe=1\alpha_e=1, and diverges logarithmically at z=±iz=\pm i. We find that the exponent relation α+2β+γ=2\alpha'+2\beta+\gamma'=2 is violated at z=1z=-1; the right-hand side is 4 rather than 2. The connections of these results with complex-temperature properties of the Ising model on the triangular lattice are discussed.Comment: 22 pages, latex, figures appended after the end of the text as a compressed, uuencoded postscript fil

    Evolution of surname distribution under gender-equality measurements

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    We consider a model for the evolution of the surnames distribution under a gender-equality measurement presently discussed in the Spanish parliament (the children take the surname of the father or the mother according to alphabetical order). We quantify how this would bias the alphabetical distribution of surnames, and analyze its effect on the present distribution of the surnames in Spain

    Series expansions without diagrams

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    We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.Comment: 24 pages, IASSNS-HEP-93/1
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