Journal article

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

AJ Guttmann, J-M Maillard

Journal of Physics A: Mathematical and Theoretical | IOP PUBLISHING LTD | Published : 2015

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

View full abstract

University of Melbourne Researchers

Grants

Awarded by Australian Research Council


Funding Acknowledgements

One of us (JMM) would like to thank G Christol for fruitful discussions on diagonals of rational functions, and discrete finite automata. A J Guttmann would like to thank the LPTMC for kind support, and gratefully acknowledges support for the Australian Research Council through grant DP140101110. This work has been performed without any support of the ANR, the ERC, the MAE or any PES of the CNRS.