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Generalized classical theory of magnetism (1987)

Pisani, Carmelo ; Thompson, Colin J.

Springer

Journal of statistical physics 46 (1987), S. 971-982

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ISSN: 1572-9613

Schlagwort(e): Kac potential ; mean-field theory ; variational principle ; helicoidal phase ; crossover ; Lifshitz point

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract We consider an Ising model with Kac potential γdK(γ¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limitγ→0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp 0≠0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2π/¦p 0¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01011152

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Digitale Medien

Asymptotic and essentially singular solutions of the Feigenbaum equation (1988)

Thompson, Colin J. ; McGuire, J. B.

Springer

Journal of statistical physics 51 (1988), S. 991-1007

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ISSN: 1572-9613

Schlagwort(e): Feigenbaum ; largeN ; iteration ; doubling transformation ; universal ; fixed point ; feigenvalue

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract For suitably defined largeN, we express Feigenbaum's equation as a singular Schroder functional equation whose solution is obtained using a scaling ansatz. In the limit of infiniteN certain self-consistency conditions on the scaled Schroder solution lead to an essentially singular solution of Feigenbaum's equation with a length scale factor of α≅ 0.0333 and. a limiting feigenvalue of δ∞≃30.50, in agreement with Eckmann and Wittwer's value of α=0.0333831... and their conjectured estimate of δ∞≲30.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01014896

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