The Stochastic complexity of spin models: How simple are simple spin models?

The Stochastic complexity of spin models: How simple are simple spin models? Alberto Beretta, 1 Claudia Battistin, 2 Cl elia de Mulatier, 1 Iacopo Mastromatteo, 3 and Matteo Marsili 1 1 The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34014 Trieste, Italy 2 Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Olav Kyrres gate 9, 7030 Trondheim, Norway 3 Capital Fund Management, 23 rue de l'Universit e, 75007 Paris, France Simple models, in information theoretic terms, are those with a small stochastic complexity. We study the stochastic complexity of spin models with interactions of arbitrary order. Invariance with respect to bijections within the space of operators allows us to classify models in complexity classes. This invariance also shows that simplicity is not related to the order of the interactions, but rather to their mutual arrangement.