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تسجيل مستخدم جديدHigh order Fuchsian equations for the square lattice Ising model: $tilde{chi}^{(5)}$
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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 corresponding linear differential operator from calculations using just a single prime. A particular linear combination of $tilde{chi}^{(1)}$ and $tilde{chi}^{(3)}$ can be removed from $tilde{chi}^{(5)}$ and the resulting series is annihilated by a high order globally nilpotent linear ODE. The corresponding (minimal order) linear differential operator, of order 29, splits into factors of small orders. A fifth order linear differential operator occurs as the left-most factor of the depleted differential operator and it is shown to be equivalent to the symmetric fourth power of $L_E$, the linear differential operator corresponding to the elliptic integral $E$. This result generalizes what we have found for the lower order terms $tilde{chi}^{(3)}$ and $tilde{chi}^{(4)}$. We conjecture that a linear differential operator equivalent to a symmetric $(n-1)$-th power of $L_E$ occurs as a left-most factor in the minimal order linear differential operators for all $tilde{chi}^{(n)}$s.
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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 suffi
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