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.
Similar content being viewed by others
References
A. Schmid,Phys. Rev. Lett. 51:1506 (1983).
P. J. Forrester,J. Stat. Phys. 51:457 (1988).
P. J. Forrester,J. Stat. Phys. 59:57 (1989).
M. L. Rosinberg, private communication.
P. J. Forrester and M. L. Rosinberg,Int. J. Phys. A, to appear.
F. J. Dyson,J. Math. Phys. 3:1191 (1962).
P. J. Forrester,J. Aust. Math. Soc. Ser. B 26:119 (1984).
T. Muir,History of the Theory of Determinants (Macmillan, London, 1911), Vol.II, p. 187.
P. A. Martin,Rev. Mod. Phys. 60:1075 (1988).
G. Gallavotti and F. Nicoló,J. Stat. Phys. 39:133 (1985).
E. R. Speer,J. Stat. Phys. 42:895 (1986).
C. N. Yang and T. D. Lee,Phys. Rev. 87:404 (1952).
H. Schultz,J. Phys. A 14:3277 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Forrester, P.J. Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases. J Stat Phys 60, 203–220 (1990). https://doi.org/10.1007/BF01013674
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01013674