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On the corrections to scaling in three-dimensional Ising models

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Abstract

The leading correction-to-scaling amplitudes for the spin-1/2, nearest-neighbor sc, bcc, and fee Ising models are considered with the particular aim of determining their signs. On the basis of previous two-variable series analyses by Chen, Fisher, and Nickel and renormalization group∈=4−d expansions, it is concluded that the correction amplitudes for the susceptibility, correlation length, specific heat, and spontaneous magnetization arenegative for all three lattices. Thus, for example, the effective exponentγ eff(T) asymptotically approaches the true susceptibility exponentγ fromabove. Other earlier and more recent high-temperature series and field-theoretic analyses are seen to be consistent with this result. However, the usual nonasymptotic, perturbative field-theoretic approaches are essentially committed to positive correction amplitudes. The question of the signs therefore relates directly to the applicability of these non-asymptotic field-theoretic calculations to three-dimensional Ising models as well as to different experimental systems.

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  1. Andrea J. Liu

    Present address: Exxon Research and Engineering Co., 08801, Annandale, New Jersey

Authors and Affiliations

  1. Institute for Physical Sciences and Technology, University of Maryland, 20742, College Park, Maryland

    Andrea J. Liu & Michael E. Fisher

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Liu, A.J., Fisher, M.E. On the corrections to scaling in three-dimensional Ising models. J Stat Phys 58, 431–442 (1990). https://doi.org/10.1007/BF01112754

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  • DOI: https://doi.org/10.1007/BF01112754

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