A Generalized Circle Theorem on Zeros of Partition Function at Asymmetric First Order Transitions
Abstract
We present a generalized circle theorem which includes the Lee-Yang theorem for symmetric transitions as a special case. It is found that zeros of the partition function can be written in terms of discontinuities in the derivatives of the free energy. For asymmetric transitions, the locus of the zeros is tangent to the unit circle at the positive real axis in the thermodynamic limit. For finite-size systems, they lie off the unit circle if the partition functions of the two phases are added up with unequal prefactors. This conclusion is substantiated by explicit calculation of zeros of the partition function for the Blume-Capel model near and at the triple line at low temperatures.
Keywords
Cite
@article{arxiv.cond-mat/9410091,
title = {A Generalized Circle Theorem on Zeros of Partition Function at Asymmetric First Order Transitions},
author = {Koo-Chul Lee},
journal= {arXiv preprint arXiv:cond-mat/9410091},
year = {2009}
}
Comments
10 pages, RevTeX. To be published in PRL. 3 Figures will be sent upon request