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Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases
Authors:P J Forrester
Institution:(1) Department of Mathematics, La Trobe University, 3083 Bundoora, Victoria, Australia
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 (xgr) plane at xgr=0, whereas in the insulating phase a neighborhood of xgr=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 couplingGamma, the zeros pinch the point xgr=0 forGamma<2, while forGammages2 a neighborhood of xgr=0 is zero free. The conductor-insulator transition therefore takes place atGamma=2 independent of the density and other parameters in the model.
Keywords:Conductor-insulator transition  Yang-Lee theory  exact solvability
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