Abstract
For the two- and three-dimensional nearest neighbors Ising model in the presence of a magnetic field, we study numerically asymptotic properties of the set of orthogonal polynomials associated with the Lee-Yang measure. This provides an insight into the nature of this measure near its end points, on the Lee-Yang circle. We introduce a smoothness index which analyzes the structure of the measure. Its value is found to be equal to 2 within 10−3 for all the models tested in two and three dimensions, at any temperatures. The results strongly suggest the absence of any singular part (continuous or pure point) in the measure, even in dimension 3. We also confirm, using a different method, known results on the behavior of the measure near its end points.
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Research Assistant of the Belgian National Fund for Scientific Research.
On leave of absence from CEN-Saclay France
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Van Assche, W., Turchetti, G. & Bessis, D. On the nature of the Lee-Yang measure for Ising ferromagnets. J Stat Phys 43, 85–108 (1986). https://doi.org/10.1007/BF01010573
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DOI: https://doi.org/10.1007/BF01010573