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Existence of free energy for models with long-range random Hamiltonians (1979)

Khanin, K. M. ; Sinai, Ya. G.

Springer

Journal of statistical physics 20 (1979), S. 573-584

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ISSN: 1572-9613

Keywords: Random interactions ; random variables ; long range ; free energy ; Hamiltonian ; spin system ; partial function

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract Classical lattice systems with random Hamiltonians $$\frac{1}{2}\sum\limits_{x_1 \ne x_2 } {\frac{{\varepsilon (x_1 ,x_2 )\varphi (x_1 )\varphi (x_2 )}}{{\left| {x_1 - x_2 } \right|^{\alpha d} }}}$$ are considered, whered is the dimension, andε(x 1,x 2) are independent random variables for different pairs (x 1,x 2),Eε(x 1,x 2) = 0. It is shown that the free energy for such a system exiists with probability 1 and does not depend on the boundary conditions, providedα 〉 1/2.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01009511

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