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

52 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 1979

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

Access to Document

10.1007/BF01009511

Cite this

@article{69a8df7cd0b540c6bb5f225154b2a77a,

title = "Existence of free energy for models with long-range random Hamiltonians",

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.\}",

year = "1979",

month = jun,

doi = "10.1007/BF01009511",

language = "English (US)",

volume = "20",

pages = "573--584",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer",

number = "6",

}

TY - JOUR

T1 - Existence of free energy for models with long-range random Hamiltonians

AU - Khanin, K. M.

AU - Sinai, Ya G.

PY - 1979/6

Y1 - 1979/6

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

UR - https://www.scopus.com/pages/publications/0009159102

UR - https://www.scopus.com/inward/citedby.url?scp=0009159102&partnerID=8YFLogxK

U2 - 10.1007/BF01009511

DO - 10.1007/BF01009511

M3 - Article

AN - SCOPUS:0009159102

SN - 0022-4715

VL - 20

SP - 573

EP - 584

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 6

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this