Phase transition between synchronous and asynchronous updating algorithms
Radicchi, F, Vilone, D, Meyer-Ortmanns, HJ. Stat. Phys. 129, 593 - 603 (2007)
Times cited: 6
Abstract
We update a one-dimensional chain of Ising spins of length L with
algorithms which are parameterized by the probability p for a certain
site to get updated in one time step. The result of the update event
itself is determined by the energy change due to the local change in
the configuration. In this way we interpolate between the Metropolis
algorithm at zero temperature when p is of the order of 1/L and L is
large, and a synchronous deterministic updating procedure for p=1. As a
function of p we observe a phase transition between the stationary
states to which the algorithm drives the system. These are
non-absorbing stationary states with antiferromagnetic domains for p >
p © , and absorbing states with ferromagnetic domains for p <= p ©
. This means that above this transition the stationary states have lost
any remnants of the ferromagnetic Ising interaction. A measurement of
the critical exponents shows that this transition belongs to the
universality class of parity conservation.