Extended Scaling for the high dimension and square lattice Ising Ferromagnets

Abstract

In the high dimension (mean field) limit the susceptibility and the second moment correlation length of the Ising ferromagnet depend on temperature as chi(T)=tau^{-1} and xi(T)=T^{-1/2}tau^{-1/2} exactly over the entire temperature range above the critical temperature T_c, with the scaling variable tau=(T-T_c)/T. For finite dimension ferromagnets temperature dependent effective exponents can be defined over all T using the same expressions. For the canonical two dimensional square lattice Ising ferromagnet it is shown that compact "extended scaling" expressions analogous to the high dimensional limit forms give accurate approximations to the true temperature dependencies, again over the entire temperature range from T_c to infinity. Within this approach there is no cross-over temperature in finite dimensions above which mean-field-like behavior sets in.

6 pages, 6 figures

References in corpus (10)

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Cited by in corpus (11)

• New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
• The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d
• Extended Scaling in High Dimensions
• An extended scaling analysis of the S=1/2 Ising ferromagnet on the simple cubic lattice
• The bimodal and Gaussian Ising Spin Glasses in dimension two revisited
• The Ising Spin Glass in dimension four
• Extended scaling for ferromagnetic Ising models with zero-temperature transitions
• The Ising universality class in dimension three: corrections to scaling
• Ising Spin Glasses in dimension five
• Large-order aspects of the delta-expansion in low-dimensional Ising models
• Hyperscaling breakdown and Ising Spin Glasses: the Binder cumulant