Abstract
Thed-dimensional, nearest-neighbor disordered Ising ferromagnet:
is studied as a function of both temperature,T, and a disorder parameter,λ, which measures the size of fluctuations of couplingsJ ij ≧0. A finite-size scaling correlation length,ζ f (T, λ), is defined in terms of the magnetic response of finite samples. This correlation length is shown to be equivalent, in the scaling sense, to the quenched average correlation lengthζ(T, λ), defined as the asymptotic decay rate of the quenched average two-point function. Furthermore, the magnetic response criterion which definesζ f is shown to have a scale-invariant property at the critical point. The above results enable us to prove that the quenched correlation length satisfies:
which implies the boundv≧2/d for the quenched correlation length exponent.
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Communicated by A. Jaffe
Work supported in part by National Science Foundation Postdoctoral Fellowships
Work supported in part by National Science Foundation Grant No. DMR-87-19523
Work supported in part by National Science Foundation Grant No. DMR-84-01225
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Chayes, J.T., Chayes, L., Fisher, D.S. et al. Correlation length bounds for disordered Ising ferromagnets. Commun.Math. Phys. 120, 501–523 (1989). https://doi.org/10.1007/BF01225510
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DOI: https://doi.org/10.1007/BF01225510