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On the density and temperature dependence of the critical behavior in non-random frozen spin clusters

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  • Poland, Douglas

Abstract

The statistical mechanics of clusters of a magnetic material (where the distribution function for the clusters is fixed and dependent on the history of the sample) in a non-magnetic matrix is studied for the plane-square lattice. The spin-configurational partition functions for small clusters are evaluated explicitly giving density and low-temperature series for the magnetic susceptibility, χ, for both random and non-random clusters. For random clusters with net density ϱ at the critical point of the pure magnetic material we find that χ goes to infinity as (1-ϱ)-32 while for non-random clusters (treated as a frozen Ising mixture) we find that χ is infinite at the double critical point (magnetic critical point and critical point for clustering).

Suggested Citation

  • Poland, Douglas, 1991. "On the density and temperature dependence of the critical behavior in non-random frozen spin clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 179(3), pages 319-339.
    • Handle: RePEc:eee:phsmap:v:179:y:1991:i:3:p:319-339
    DOI: 10.1016/0378-4371(91)90082-N
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    1. Lebowitz, Michael A., 1968. "Canada's First Bank: A History of the Bank of Montreal. By Merrill Denison. Two Volumes. New York: Dodd, Mead & Co., 1966, 1967. Pp. xix, 472; xiii, 454. $7.50 each," The Journal of Economic History, Cambridge University Press, vol. 28(4), pages 660-661, December.
    2. Velgakis, M.J., 1989. "Site-diluted two-dimensional Ising models with competing interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 159(2), pages 167-169.
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