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تسجيل مستخدم جديدAutomata and the susceptibility of the square lattice Ising model modulo powers of primes
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We study the full susceptibility of the Ising model modulo powers of primes. We find exact functional equations for the full susceptibility modulo these primes. Revisiting some lesser-known results on discrete finite automata, we show that these results can be seen as a consequence of the fact that, modulo 2^r, one cannot distinguish the full susceptibility from some simple diagonals of rational functions which reduce to algebraic functions modulo 2^r, and, consequently, satisfy exact functional equations modulo 2^r. We sketch a possible physical interpretation of these functional equations modulo 2^r as reductions of a master functional equation corresponding to infinite order symmetries such as the isogenies of elliptic curves. One relevant example is the Landen transformation which can be seen as an exact generator of the Ising model renormalization group. We underline the importance of studying a new class of functions corresponding to ratios of diagonals of rational functions: they reduce to algebraic functions modulo powers of primes and they may have solutions with natural boundaries.
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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 calcula
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We study the class of non-holonomic power series with integer coefficients that reduce, modulo primes, or powers of primes, to algebraic functions. In particular we try to determine whether the susceptibility of the square-lattice Ising model belongs
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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
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