Transfer operator analysis of the parallel dynamics of disordered Ising chains

Anthonius Coolen (1) , Koujin Takeda (2)

1 London Institute for Mathematical Sciences
2 Department of Computational Intelligence and Systems Science

We study the synchronous stochastic dynamics of the random field and random bond Ising chain. For this model the generating functional analysis method of De Dominicis leads to a formalism with transfer operators, similar to transfer matrices in equilibrium studies, but with dynamical paths of spins and (conjugate) fields as arguments, as opposed to replicated spins. In the thermodynamic limit the macroscopic dynamics is captured by the dominant eigenspace of the transfer operator, leading to a relative simple and transparent set of equations that are easy to solve numerically. Our results are supported excellently by numerical simulations.

Mots clés: Physical Sciences

Domaines: Matière Condensée [cond-mat]

Anthonius Coolen, Koujin Takeda. Transfer operator analysis of the parallel dynamics of disordered Ising chains. Philosophical Magazine, 2011, pp.1. ⟨10.1080/14786435.2011.606238⟩. ⟨hal-00726662⟩