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

Abstract

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 2r, one cannot distinguish the full susceptibility from some simple diagonals of rational functions which reduce to algebraic functions modulo 2r, and, consequently, satisfy exact functional equations modulo 2r. We sketch a possible physical interpretation of these functional equations modulo 2r as reductions of a master functional equation corresponding to infinite order symmetries such a..