https://doi.org/10.1007/s100510070108
Weakly nonextensive thermostatistics and the Ising model with long-range interactions
1
Departament de Física, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain
2
Faculty of Astronomy and Geophysics, National University La Plata, Casilla de Correo 727, La Plata 1900, Argentina
3
CONICET, Casilla de Correo 727, La Plata 1900, Argentina
4
Instituto Mediterraneo de Estudios Avanzados (IMEDEA),
Campus UIB, 07071 Palma de Mallorca, Spain
Received:
24
May
2000
Published online: 15 October 2000
We introduce a new nonextensive entropic measure that grows
like
, where N is the size of the system under
consideration. This kind of nonextensivity arises in a natural way in
some N-body systems endowed with long-range interactions described
by
interparticle potentials. The power law (weakly
nonextensive) behavior exhibited by
is intermediate between
(1) the linear (extensive) regime characterizing the standard
Boltzmann-Gibbs entropy and (2) the exponential law (strongly
nonextensive) behavior associated with the Tsallis generalized
q-entropies. The functional
is parametrized by the real
number
in such a way that the standard logarithmic
entropy is recovered when
. We study the mathematical
properties of the new entropy, showing that the basic requirements for
a well behaved entropy functional are verified, i.e.,
possesses the usual properties of positivity, equiprobability,
concavity and irreversibility and verifies Khinchin axioms except the
one related to additivity since
is nonextensive. For
, the entropy
becomes superadditive in the
thermodynamic limit. The present formalism is illustrated by a
numerical study of the thermodynamic scaling laws of a ferromagnetic
Ising model with long-range interactions.
75.10.Hk Classical spin models
PACS: 05.20.-y – Classical statistical mechanics / 05.20.Gg – Classical ensemble theory / 02.70.Lq – Monte Carlo and statistical methods
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000