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  • 1
    Electronic Resource
    Electronic Resource
    The two-dimensional one-component plasma at Γ=2: Behavior of correlation functions in strip geometry (1983)
    Springer
    Journal of statistical physics 31 (1983), S. 129-140 
    Details
    ISSN: 1572-9613
    Keywords: Coulomb systems ; plasmas ; surface properties ; strip geometry ; correlations ; sum rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper considers a strip of two-dimensional one-component plasma of particles of chargeq at a temperatureT such that the coupling constant be Γ=q2/kBT = 2. The strip is of finite width and infinite length and bears charge densities on either edge. Inside the strip and on one side, the dielectric constant is 1; on the other side of the strip, it may be either 1 or 0 (in the latter case, image forces play an important role). The free energy as well as the one-particle and two-particle distribution functions can be exactly computed. They obey a variety of sum rules reflecting the Coulombic behavior of the system. At large separations the truncated two-particle distribution function behaves with algebraically decaying oscillations. The strip of finite width in fact is correlated along the strip much as a one-dimensional system is correlated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010926
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Finite-size corrections to the free energy of Coulomb systems with a periodic boundary condition (1991)
    Springer
    Journal of statistical physics 63 (1991), S. 491-504 
    Details
    ISSN: 1572-9613
    Keywords: Coulomb systems ; finite-size corrections ; sine-Gordon field theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Classical Coulomb systems ind dimensions (d⩾2) with a periodic boundary condition, periodW, in the directionx (d)are considered. With the other directions of the confining volume of lengthL, it is shown that if the system is in a conducting phase, then the “strip” free energykTf W ,f W = −lim L→∞ L −(d−1) log Z, has the large-W expansion $$f_W \sim Wf_\infty + \frac{{(d/2 - 1)\Gamma (d/2 - 1)}}{{\pi ^{d/2} W^{d - 1} }}\zeta (d) + O\left( {\frac{1}{{W^{d + 1} }}} \right)$$ wherekTf ∞ is the bulk free energy per unit volume, ζ(x) denotes the Riemann zeta function, andΓ(x) denotes the gamma function. With 1/W identified askT, this result is precisely the low-temperature behavior of the free energy of a (d−1)-dimensional Debye solid. This fact is explained in terms of an equivalence between the Coulomb gas and quantum fields. Also, the expansion is verified for some exactly solved models of Coulomb systems in two dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029197
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Universality in some classical Coulomb systems of restricted dimension (1996)
    Springer
    Journal of statistical physics 84 (1996), S. 359-378 
    Details
    ISSN: 1572-9613
    Keywords: Universality ; Coulomb systems ; finite-size effects ; solvable models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Coulomb systems in which the particles interact through thed-dimensional Coulomb potential but are confined in a flat manifold of dimensiond−1 are considered. The actual Coulomb potential acting is defined by particular boundary conditions involving a characteristic macroscopic distanceW in the direction perpendicular to the manifold: either it is periodic of periodW in that direction, or it vanishes on one ideal conductor wall parallel to the manifold at a distanceW from it, or it vanishes on two parallel walls at a distanceW from each other with the manifold equidistant from them. Under the assumptions that classical equilibrium statistical mechanics is applicable and that the system has the macroscopic properties of a conductor, it is shown that the suitably smoothed charge correlation function is universal, and that the free energy and the grand potential have universal dependences onW (universal means independent of the microscopic detail). The casesd=2 are discussed in detail, and the generic results are checked on an exactly solvable model. The cased=3 of a plane parallel to an ideal conductor is also explicitly worked out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02179647
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    Paper (German National Licenses)
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  • 4
    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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  • 5
    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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