Zobrazeno 1 - 10
of 88
pro vyhledávání: '"Zenine, N."'
This paper is a plea for diagonals and telescopers of rational, or algebraic, functions using creative telescoping, in a computer algebra experimental mathematics learn-by-examples approach. We show that diagonals of rational functions (and this is a
Externí odkaz:
http://arxiv.org/abs/2310.06963
We previously reported on a recursive method to generate the expansion of the lattice Green function of the $d$-dimensional face-centred cubic lattice (fcc). The method was used to generate many coefficients for d=7 and the corresponding linear diffe
Externí odkaz:
http://arxiv.org/abs/1601.05657
Autor:
Bostan, A., Boukraa, S., Hassani, S., van Hoeij, M., Maillard, J. -M., Weil, J-A., Zenine, N.
We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contribution of the susceptibility of the Ising model for $\, n \le 6$, are operators "associated with elliptic curves". Beyond the simplest
Externí odkaz:
http://arxiv.org/abs/1007.0535
We review developments made since 1959 in the search for a closed form for the susceptibility of the Ising model. The expressions for the form factors in terms of the nome $q$ and the modulus $k$ are compared and contrasted. The $\lambda$ generalized
Externí odkaz:
http://arxiv.org/abs/1003.0751
Autor:
Nickel, B., Jensen, I., Boukraa, S., Guttmann, A. J., Hassani, S., Maillard, J. -M., Zenine, N.
We obtain in exact arithmetic the order 24 linear differential operator $L_{24}$ and right hand side $E^{(5)}$ of the inhomogeneous equation$L_{24}(\Phi^{(5)}) = E^{(5)}$, where $\Phi^{(5)} =\tilde{\chi}^{(5)}-\tilde{\chi}^{(3)}/2+\tilde{\chi}^{(1)}/
Externí odkaz:
http://arxiv.org/abs/1002.0161
This paper deals with $\tilde{\chi}^{(6)}$, the six-particle contribution to the magnetic susceptibility of the square lattice Ising model. We have generated, modulo a prime, series coefficients for $\tilde{\chi}^{(6)}$. The length of the series is s
Externí odkaz:
http://arxiv.org/abs/0912.4968
Autor:
Bostan, A., Boukraa, S., Hassani, S., Maillard, J. -M., Weil, J-A., Zenine, N., Abarenkova, N.
We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization group.
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Externí odkaz:
http://arxiv.org/abs/0911.5466
Autor:
Bostan, A., Boukraa, S., Guttmann, A. J., Hassani, S., Jensen, I., Maillard, J. -M., Zenine, N.
We consider the Fuchsian linear differential equation obtained (modulo a prime) for $\tilde{\chi}^{(5)}$, the five-particle contribution to the susceptibility of the square lattice Ising model. We show that one can understand the factorization of the
Externí odkaz:
http://arxiv.org/abs/0904.1601
We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions a
Externí odkaz:
http://arxiv.org/abs/0812.4931
Autor:
Boukraa, S., Guttmann, A. J., Hassani, S., Jensen, I., Maillard, J. -M., Nickel, B., Zenine, N.
Publikováno v:
J.Phys.A41:455202,2008
We calculate very long low- and high-temperature series for the susceptibility $\chi$ of the square lattice Ising model as well as very long series for the five-particle contribution $\chi^{(5)}$ and six-particle contribution $\chi^{(6)}$. These calc
Externí odkaz:
http://arxiv.org/abs/0808.0763