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

K. M. Khanin, Ya G. Sinai

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


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 languageEnglish (US)
Pages (from-to)573-584
Number of pages12
JournalJournal of Statistical Physics
Issue number6
StatePublished - Jun 1 1979
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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


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