| Numéro |
J. Phys. I France
Volume 4, Numéro 11, November 1994
|
|
|---|---|---|
| Page(s) | 1597 - 1617 | |
| DOI | https://doi.org/10.1051/jp1:1994210 | |
J. Phys. I France 4 (1994) 1597-1617
Ferrimagnetism in a disordered Ising model
Giovanni Paladin1, Michele Pasquini1 and Maurizio Serva21 Dipartimento di Fisica, Università dell' Aquila, 1-67100 Coppito, L'Aquila, Italy
2 Dipartimento di Matematica, Università dell' Aquila, 1-67100 Coppito, L'Aquila, Italy
(Received 20 May 1994, accepted 3 August 1994)
Abstract
We introduce a one dimensional Ising model with two competing interactions : nearest neighbor
random couplings
with equal probability and a positive infinite range coupling
. At low temperature
T the model exhibits a first order phase transition between a
ferromagnetic state (with magnetization
m1 = 1 at
T = 0) and a " ferrimagnetic " state
(with
m2= 2/3 at
T = 0), when the disorder strength
is increased. For 5/12
, a whole spectrum of ferrimagnetic ground states with magnetization
mn =
2/(n + 1) (
n = 2,
,
) is present while for
the ground state
is given by a trivial one dimensional spin glass with
m = 0. The main qualitative features
of the model can be described by a simplified annealed model where the random couplings can
arrange themselves to minimize free energy with the constraint that the number of positive
couplings is fixed by the law of large numbers in the thermodynamic limit. This model is
exactly solved at all temperatures and the diagram of phase is calculated.
© Les Editions de Physique 1994