1 research outputs found
Long-range interactions and non-extensivity in ferromagnetic spin models
The Ising model with ferromagnetic interactions that decay as is
analyzed in the non-extensive regime , where the
thermodynamic limit is not defined. In order to study the asymptotic properties
of the model in the limit ( being the number of spins)
we propose a generalization of the Curie-Weiss model, for which the
limit is well defined for all . We
conjecture that mean field theory is {\it exact} in the last model for all
. This conjecture is supported by Monte Carlo heat bath
simulations in the case. Moreover, we confirm a recently conjectured
scaling (Tsallis\cite{Tsallis}) which allows for a unification of extensive
() and non-extensive () regimes.Comment: RevTex, 12 pages, 1 eps figur