Automata and the susceptibility of the square lattice Ising model modulo powers of primes

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