YANG-LEE EDGE SINGULARITIES AT HIGH-TEMPERATURES

The density of Lee-Yang zeros, in the thermodynamic limit, for classical n-vector models and for the quantum Heisenberg model is studied in the asymptotic high-temperature limit. It is shown that the high-temperature series expansions for these models reduce, in this limit, to the corresponding low-density expansions for the monomer-dimer problem with negative dimer activity. If the density of zeros, g(h), on the imaginary axis of the complex reduced-magnetic-field plane, h=HkBT=h+ih, has an algebraic singularity at the edge of the gap in the zero distribution, g(h)[|h|-h0(T)], then is independent of n in this limit. Analyzing dimer density series on various lattices by means of the ratio test, Dlog Padé, the recursion-relation method, and inhomogeneous differential approximants, we obtain the estimates =-0.163 for d=2 dimensions and =0.08615 for d=3. © 1979 The American Physical Society.