2006/11/21 by Filippo Radicchi, Daniele Vilone, Hildegard Meyer-Ortmanns
Computer Science · Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Quantum Computing Algorithms and Architecture #Theoretical and Computational Physics #cond-mat.other
paper · pdf · doi:10.1007/s10955-007-9416-8
published as J. Stat. Phys. 129, 593-603 (2007) · 5 pages, 3 figures
arxiv created 2006/11/21 · openalex publication_date 2007/09/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 for p of the order of 1/L and for large L, and a synchronous deterministic updating procedure for p=1. As 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>pc, and absorbing states with ferromagnetic domains for p≤ pc. This means that above this transition the stationary states have lost any remnants to the ferromagnetic Ising interaction. A measurement of the critical exponents shows that this transition belongs to the universality class of parity conservation.