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- W3101780273 endingPage "494010" @default.
- W3101780273 startingPage "494010" @default.
- W3101780273 abstract "Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables above Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $ chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $ chi^{(3)}$ and $ chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility." @default.
- W3101780273 created "2020-11-23" @default.
- W3101780273 creator A5010858529 @default.
- W3101780273 creator A5031296793 @default.
- W3101780273 creator A5039262903 @default.
- W3101780273 date "2012-11-27" @default.
- W3101780273 modified "2023-10-16" @default.
- W3101780273 title "Holonomic functions of several complex variables and singularities of anisotropic Isingn-fold integrals" @default.
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- W3101780273 doi "https://doi.org/10.1088/1751-8113/45/49/494010" @default.
- W3101780273 hasPublicationYear "2012" @default.
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