Abstract
The distribution of zeros of the partition function in the complex magnetic field plane is studied for linear chains ofn-vector spins and finite-width strips of Ising spins with nearest-neighbor interactions. By means of transfer matrix/operator techniques, the exponent σ characterizing the behavior of the density of zeros near the Yang-Lee edge is shown to have the exact valuea =−1/2 (i) analytically forn-vector chains in the high-temperature limit and for Ising strips in the low-temperature limit, and (ii) numerically for intermediate temperatures. The crossover of σ from itsn-vector value to its spherical model value, σ = 1/2, asn → ∞, as well as fromd = 1 tod = 2 Ising as the width of the strips increases, seems to proceed by an accumulation of branch points in the spectrum of the transfer operator; for then-vector models the position of the gap edge and the free energy at the edge approach their spherical model values with corrections of order l/n ζ with ζ ≅ 3/4.
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Kurtze, D.A. The Yang-Lee edge singularity in one-dimensional Ising andN-vector models. J Stat Phys 30, 15–35 (1983). https://doi.org/10.1007/BF01010866
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DOI: https://doi.org/10.1007/BF01010866