plied by a power of p . It is possible that a different choice of factor would produce better results in the case of 2- and 3-dimensional lattices. We believe that what is said here for the Ising model also goes for other models, i.e. the magnetisation distribution for quantum spin models or for spin-glass models can be modeled by p, q -binomial distributions. Acknowledgments One of the authors (AR) wishes to thank the Swedish Research Council (VR) for financing this work. This research was conducted using the resources of High Performance Computing Center North (HPC2N). ∗ Electronic address: phl@kth.se † Electronic address: roseng@kth.se 1 G. Gasper and M. Rahman, Basic hypergeometric series , vol. 96 of Encyclopedia of mathematics and its applications (Cambridge Univerity Press, Cambridge, UK, 2004), 2nd ed. 2 G. E. Andrews, The theory of partitions , vol. 2 of Encyclopedia of mathematics and its applica- tions (Addison-Wesley, Reading, Massachusetts, 1976). 3 G. E. Andrews, R. Askey, and R. Roy, Special functions , vol. 71 of Encyclopedia of mathematics and its applications (Cambridge University Press, Cambridge, UK, 1999). 4 G. E. Andrews, q -series: their development and application in analysis, number theory, combi- natorics, physics, and computer algebra , vol. 66 of Regional conference series in mathematics (American Mathematical Society, Providence, Rhode Island, 1986). 5 R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete mathematics: a foundation for com- puter science (Addison-Wesley, Reading, Massachusetts, 1994), 2nd ed. 6 R. B. Corcino, INTEGERS: Electronic journal of combinatorial number theory 8 , #A29 (2008). 7 L. M. Butler, J. Combin. Theory A 54 , 54 (1990). 8 C. Krattenthaler, Monatsh. Math. 107 , 333 (1989). 9 L. M. Kirousis, Y. C. Stamatiou, and M. Vamvakari, Stud. Appl. Math. 107 , 43 (2001). 50