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  • 1
    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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  • 2
    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)
    Fulltext
  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    Classical Skew Orthogonal Polynomials and Random Matrices (2000)
    Springer
    Journal of statistical physics 99 (2000), S. 141-170 
    Details
    ISSN: 1572-9613
    Keywords: random matrices ; correlation functions ; orthogonal polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Skew orthogonal polynomials arise in the calculation of the n-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely determined by a certain sum involving the skew orthogonal polynomials. In the case that the eigenvalue probability density function involves a classical weight function, explicit formulas for the skew orthogonal polynomials are given in terms of related orthogonal polynomials, and the structure is used to give a closed-form expression for the sum. This theory treates all classical cases on an equal footing, giving formulas applicable at once to the Hermite, Laguerre, and Jacobi cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018644606835
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    Paper (German National Licenses)
    Fulltext
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