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  • 1
    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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  • 2
    Electronic Resource
    Electronic Resource
    Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases (1990)
    Springer
    Journal of statistical physics 60 (1990), S. 203-220 
    Details
    ISSN: 1572-9613
    Keywords: Conductor-insulator transition ; Yang-Lee theory ; exact solvability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A feature of a conducting phase at low density is that there is a singularity in the fugacity expansion of the pressure, whereas the same expansion in the insulating phase gives an analytic series. The Yang-Lee characterization of a phase transition thus implies that in the conducting phase the zeros of the grand partition function must pinch the real axis in the complex scaled fugacity (ξ) plane at ξ=0, whereas in the insulating phase a neighborhood of ξ=0 must be zero free. Exact and numerical calculations are presented which suggest that for two-component log-potential lattice gases in one dimension with dimensionless couplingΓ, the zeros pinch the point ξ=0 forΓ〈2, while forΓ⩾2 a neighborhood of ξ=0 is zero free. The conductor-insulator transition therefore takes place atΓ=2 independent of the density and other parameters in the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01013674
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Exact results for the two-dimensional, two-component plasma atΓ=2 in doubly periodic boundary conditions (1990)
    Springer
    Journal of statistical physics 61 (1990), S. 1141-1160 
    Details
    ISSN: 1572-9613
    Keywords: Two-component plasma ; determinants ; Yang-Lee theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The two-dimensional, two-component plasma is considered in doubly periodic boundary conditions with the positive and negative charges confined to separate interlacing rectangular lattices. It is shown that at the special couplingΓ=2, on a lattice of 2M 1×2M 2 sites, the grand partition function can be written as a double integral over a product of determinants of dimension 2M 2×2M 2. On the basis of a conjecture regarding the zero distribution of the grand partition function, the large-M 2 behavior of the determinant is given and the pressure evaluated exactly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01014369
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    Paper (German National Licenses)
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  • 4
    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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  • 5
    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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