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) |
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Pages (from-to) | 573-584 |
Number of pages | 12 |
Journal | Journal of Statistical Physics |
Volume | 20 |
Issue number | 6 |
DOIs | |
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