Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases |
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Authors: | P J Forrester |
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Institution: | (1) Department of Mathematics, La Trobe University, 3083 Bundoora, Victoria, Australia |
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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 () plane at =0, whereas in the insulating phase a neighborhood of =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 coupling, the zeros pinch the point =0 for<2, while for2 a neighborhood of =0 is zero free. The conductor-insulator transition therefore takes place at=2 independent of the density and other parameters in the model. |
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Keywords: | Conductor-insulator transition Yang-Lee theory exact solvability |
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