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

K. M. Khanin; Ya G. Sinai

doi:10.1007/BF01009511

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

K. M. Khanin, Ya G. Sinai

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

Classical lattice systems with random Hamiltonians {Mathematical expression} are considered, where d is the dimension, and ε(x₁, x₂) are independent random variables for different pairs (x₁, x₂), Eε(x₁, x₂) = 0. It is shown that the free energy for such a system exiists with probability 1 and does not depend on the boundary conditions, provided α > 1/2.

Original language	English (US)
Pages (from-to)	573-584
Number of pages	12
Journal	Journal of Statistical Physics
Volume	20
Issue number	6
DOIs	https://doi.org/10.1007/BF01009511
State	Published - Jun 1 1979
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

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

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10.1007/BF01009511

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abstract = "Classical lattice systems with random Hamiltonians {Mathematical expression} are considered, where d is the dimension, and ε(x1, x2) are independent random variables for different pairs (x1, x2), Eε(x1, x2) = 0. It is shown that the free energy for such a system exiists with probability 1 and does not depend on the boundary conditions, provided α > 1/2.",

keywords = "Hamiltonian, Random interactions, free energy, long range, partial function, random variables, spin system",

author = "Khanin, {K. M.} and Sinai, {Ya G.}",

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AU - Khanin, K. M.

AU - Sinai, Ya G.

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N2 - Classical lattice systems with random Hamiltonians {Mathematical expression} are considered, where d is the dimension, and ε(x1, x2) are independent random variables for different pairs (x1, x2), Eε(x1, x2) = 0. It is shown that the free energy for such a system exiists with probability 1 and does not depend on the boundary conditions, provided α > 1/2.

AB - Classical lattice systems with random Hamiltonians {Mathematical expression} are considered, where d is the dimension, and ε(x1, x2) are independent random variables for different pairs (x1, x2), Eε(x1, x2) = 0. It is shown that the free energy for such a system exiists with probability 1 and does not depend on the boundary conditions, provided α > 1/2.

KW - Hamiltonian

KW - Random interactions

KW - free energy

KW - long range

KW - partial function

KW - random variables

KW - spin system

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ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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