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  • 1
    Electronic Resource
    Electronic Resource
    A testbench for the nested dipole hypothesis of Kosterlitz and Thouless (1995)
    Springer
    Journal of statistical physics 79 (1995), S. 503-523 
    Details
    ISSN: 1572-9613
    Keywords: Kosterlitz-Thouless transition ; Coulomb gas ; renormalization equations ; correlations ; exact solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the two-dimensional one-component plasma without a background and confined to a half-plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wall with an inverse-power-law Boltzmann factor. The model has a known solvable isotherm which exhibits a Kosterlitz-Thouless-type transition from a conductive to an insulator phase as the power law is varied. This allows predictions of theoretical methods of analyzing the Kosterlitz-Thouless transition to be compared with the exact solution. In particular, we calculate the asymptotic density profile by resumming its low-fugacity expansion near the zero-density critical coupling in the insulator phase, and solving a mean-field equation deduced from the first BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesis of Kosterlitz and Thouless, the validity of this hypothesis is explicitly verified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02184869
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The two-dimensional Coulomb gas on a sphere: Exact results (1992)
    Springer
    Journal of statistical physics 69 (1992), S. 179-192 
    Details
    ISSN: 1572-9613
    Keywords: Coulomb gas ; solvable models ; Dirac equation ; curved space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract At the special value of the reduced inverse temperatureΓ=2, the equilibrium statistical mechanics of a two-dimensional Coulomb gas confined to the surface of a sphere is an exactly solvable problem, just as it was for the Coulomb gas in a plane. The thermodynamic quantities and all the correlation functions can be calculated. Use is made of an isomorphism between the classical Coulomb gas and the free Fermi field theory associated with the Dirac operator on the sphere.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053789
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The two-dimensional two-component plasma plus background on a sphere: Exact results (1996)
    Springer
    Journal of statistical physics 84 (1996), S. 337-357 
    Details
    ISSN: 1572-9613
    Keywords: Coulomb gas ; solvable models ; finite-size corrections
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made up of a uniformly charged background, positive particles, and negative particles, on the surface of a sphere. At the special value Γ=2 of the reduced inverse temperature, the classical equilibrium statistical mechanics is worked out: the correlations and the grand potential are calculated. The thermodynamic limit is taken, and as it is approached the grand potential exhibits a finite-size correction of the expected universal form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02179646
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Exact Finite-Size Study of the 2D OCP at Γ=4 and Γ=6 (1999)
    Springer
    Journal of statistical physics 97 (1999), S. 489-521 
    Details
    ISSN: 1572-9613
    Keywords: Coulomb gas ; one-component plasma ; symmetric polynomials ; finite-size corrections ; second-moment sum rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An exact numerical study is undertaken into the finite-N calculation of the free energy and distribution functions for the two-dimensional one-component plasma. Both disk and sphere geometries are considered, with the coupling Γ set equal to 4 and 6. Extrapolation of our data for the free energy is consistent with the existence of a universal term (χ/12)logN, where χ denotes the Euler characteristic of the surface, as predicted theoretically. The exact finite-N density profile is shown to give poor agreement with the contact theorem relating the density at contact and potential drop to the pressure in the thermodynamic limit. This is understood theoretically via a known finite-N version of the contact theorem. Furthermore, the ideas behind the derivation of the latter result are extended to give a sum rule for the second moment of the pair correlation in the finite disk, which in the thermodynamic limit converges to the Stillinger–Lovett result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004654923170
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Vicious random walkers in the limit of a large number of walkers (1989)
    Springer
    Journal of statistical physics 56 (1989), S. 767-782 
    Details
    ISSN: 1572-9613
    Keywords: Random walk ; Coulomb gas ; orthogonal polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The vicious random walker problem on a line is studied in the limit of a large number of walkers. The multidimensional integral representing the probability that thep walkers will survive a timet (denotedP t (p) ) is shown to be analogous to the partition function of a particular one-component Coulomb gas. By assuming the existence of the thermodynamic limit for the Coulomb gas, one can deduce asymptotic formulas forP t (p) in the large-p, large-t limit. A straightforward analysis gives rigorous asymptotic formulas for the probability that after a timet the walkers are in their initial configuration (this event is termed a reunion). Consequently, asymptotic formulas for the conditional probability of a reunion, given that all walkers survive, are derived. Also, an asymptotic formula for the conditional probability density that any walker will arrive at a particular point in timet, given that allp walkers survive, is calculated in the limitt≫p.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01016779
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    Paper (German National Licenses)
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