3 research outputs found
On the -binomial distribution and the Ising model
A completely new approach to the Ising model in 1 to 5 dimensions is
developed. We employ -binomial coefficients, a generalisation of the
binomial coefficients, to describe the magnetisation distributions of the Ising
model. For the complete graph this distribution corresponds exactly to the
limit case . We take our investigation to the simple -dimensional
lattices for and fit -binomial distributions to our data,
some of which are exact but most are sampled. For and the
magnetisation distributions are remarkably well-fitted by -binomial
distributions. For we are only slightly less successful, while for
we see some deviations (with exceptions!) between the -binomial
and the Ising distribution. We begin the paper by giving results on the
behaviour of the -distribution and its moment growth exponents given a
certain parameterization of . Since the moment exponents are known for the
Ising model (or at least approximately for ) we can predict how
should behave and compare this to our measured . The results speak in
favour of the -binomial distribution's correctness regarding their general
behaviour in comparison to the Ising model. The full extent to which they
correctly model the Ising distribution is not settled though.Comment: 51 pages, 23 figures, submitted to PRB on Oct 23 200