Partition function zeros for the one-dimensional ordered plasma in Dirichlet boundary conditions |
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Authors: | J Roumeliotis E R Smith |
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Institution: | (1) Mathematics Department, La Trobe University, 3083 Bundoora, Victoria, Australia;(2) Mathematics Department, University College, Australian Defence Forces Academy, 2601 Campbell, ACT, Australia;(3) Mathematics Department, Odense University, 5230 Odense M, Denmark |
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Abstract: | We consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacity 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 the plane occupy the imaginary axis from –i to –ic and ic to i for some c. They also occupy the diamond shape of four straight lines from ±ic to c and from ±ic to –c. The fugacity 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. |
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Keywords: | Partition function zeros mean field transition one-dimensional plasma |
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