Integral Kernel of the Spin Glass Integral Equation for the Bethe Lattice | Zendy

Mitsuhiro Seino | Zendy; Shigetoshi Katsura | Zendy

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Integral Kernel of the Spin Glass Integral Equation for the Bethe Lattice

Author(s) -

Mitsuhiro Seino,

Shigetoshi Katsura

Publication year - 1994

Publication title -

progress of theoretical physics supplement

Language(s) - English

Resource type - Journals

ISSN - 0375-9687

DOI - 10.1143/ptps.115.237

Subject(s) - integral equation , fourier transform , hypergeometric function , mathematical physics , lattice (music) , kernel (algebra) , spin glass , mathematics , hypergeometric distribution , condensed matter physics , physics , mathematical analysis , pure mathematics , acoustics

The integral equation for the distribution function g(h) of the effective field h is investigated. The Fourier transform S(x) of g(h) satisfies S(x) = (1/2π)∫ − ∞∞K(x, y) [S(y)] z−1 dy. The kernel K(x, y) which has been given by a double integral previously, is evaluated in terms of the hypergeometric functions. The behavior of K(x, y) is shown for various values of the temperatures. The result suggests that g(h) does not vary much below the spin glass transition temperature from the one at the temperature zero

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