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)]^σ, then σ is independent of n in this limit. Analyzing dimer density series on various lattices by means of the ratio test, Dlog Pad\'e, the recursion-relation method, and inhomogeneous differential approximants, we obtain the estimates σ=-0.163±3 for $d=2$ dimensions and σ=0.086±15 for $d=3$.