On the p, q -binomial distribution and the Ising model P. H. Lundow ∗ and A. Rosengren † Condensed Matter Theory, Department of Theoretical Physics, AlbaNova University Center, KTH, SE-106 91 Stockholm, Sweden (Dated: October 31, 2018) A completely new approach to the Ising model in 1 to 5 dimensions is developed. We employ p, q -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 p = q . We take our investigation to the simple d -dimensional lattices for d = 1 , 2 , 3 , 4 , 5 and fit p, q -binomial distributions to our data, some of which are exact but most are sampled. For d = 1 and d = 5 the magnetisation distributions are remarkably well-fitted by p, q -binomial distributions. For d = 4 we are only slightly less successful, while for d = 2 , 3 we see some deviations (with exceptions!) between the p, q -binomial and the Ising distribution. We begin the paper by giving results on the behaviour of the p, q -distribution and its moment growth exponents given a certain parameterization of p, q . Since the moment exponents are known for the Ising model (or at least approximately for d = 3) we can predict how p, q should behave and compare this to our measured p, q . The results speak in favour of the p, q -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. 1 arXiv:1001.2903v1 [cond-mat.stat-mech] 17 Jan 2010 Abstract