Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases

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.