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Partition function zeros for the one-dimensional ordered plasma in Dirichlet boundary conditions (1992)

Roumeliotis, J. ; Smith, E. R.

Springer

Journal of statistical physics 66 (1992), S. 233-247

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ISSN: 1572-9613

Schlagwort(e): Partition function zeros ; mean field transition ; one-dimensional plasma

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract We consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacityζ in an applied electric fieldE with Dirichlet boundary conditions. The system has a phase transition from a low-coupling phase with equally spaced particles to a high-coupling phase with particles clustered into dipolar pairs. An exact expression for the partition function is developed. In zero applied field the zeros in theζ plane occupy the imaginary axis from −i∞ to −iζc and iζc to i∞ for some ζc. They also occupy the diamond shape of four straight lines from ±iζc to ζc and from ±iζc to −ζc. The fugacityζ acts like a temperature or coupling variable. The symmetry-breaking field is the applied electric fieldE. A finite-size scaling representation for the partition in scaled coupling and scaled electric field is developed. It has standard mean field form. When the scaled coupling is real, the zeros in the scaled field lie on the imaginary axis and pinch the real scaled field axis as the scaled coupling increases. The scaled partition function considered as a function of two complex variables, scaled coupling and scaled field, has zeros on a two-dimensional surface in a domain of four real variables. A numerical discussion of some of the properties of this surface is presented.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01060066

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Digitale Medien

Lee-Yang zeros and stokes phenomenon in a model with a wetting transition (1993)

Pisani, C. ; Smith, E. R.

Springer

Journal of statistical physics 72 (1993), S. 51-78

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ISSN: 1572-9613

Schlagwort(e): Partition function zeros ; Stokes phenomenon ; wetting transition

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract We consider the statistical mechanics of a fluctuating string (1D solid-on-solid model) ofN columns with a contact energy term displaying a critical wetting transition. For this model we derive a contour integral representation for the finite-size partition function. From this representation we derive a polynomial representation and obtain the Lee-Yang zeros forN ≲, 100. Through the asymptotic evaluation of the contour integral we evaluate the zeros for higherN. This asymptotic evaluation displays a Stokes phenomenon providing a different viewpoint of the mechanism by which a phase transition can arise, supplementing the picture of Lee and Yang. We also reproduce and extend somewhat the results of Smith for the finite-size scaling limit of the partition function.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01048040

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