Transfer operator analysis of the parallel dynamics of disordered Ising chains

TY - JOUR

T1 - Transfer operator analysis of the parallel dynamics of disordered Ising chains

AU - Coolen, Anthony C. C.

AU - Takeda, Koujin

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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 relatively simple and transparent set of equations that are easy to solve numerically. Our results are supported excellently by numerical simulations.

AB - 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 relatively simple and transparent set of equations that are easy to solve numerically. Our results are supported excellently by numerical simulations.

U2 - 10.1080/14786435.2011.606238

DO - 10.1080/14786435.2011.606238

M3 - Article

VL - 92

SP - 64

EP - 77

JO - PHILOSOPHICAL MAGAZINE

JF - PHILOSOPHICAL MAGAZINE

IS - 1-3

ER -