Nonequilibrium Ising models with competing, reaction-diffusion dynamics
Open Access
- 1 November 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 40 (10), 5802-5814
- https://doi.org/10.1103/physreva.40.5802
Abstract
We study the phase diagram and other general macroscopic properties of an interacting spin (or particle) system out of equilibrium, namely, a reaction-diffusion Ising model whose time evolution occurs as a consequence of a combination of spin-flip (Glauber) and spin-exchange (Kawasaki) processes. The Glauber rate at site x when the configuration is s, say c(s;x), satisfies detailed balance at a reciprocal temperature β, while the Kawasaki rate for the interchange between nearest-neighbor sites x and y, Γc(s;x,y), satisfies detailed balance at temperature β’. We derive hydrodynamic-type macroscopic equations from the stochastic microscopic model for β’,β≥0 and large Γ when time and space are rescaled by Γ and √Γ , respectively, and study the homogeneous steady solutions of those equations when Γ→∞. We state some general theorems for β’=0 and solve explicitly the model with different choices c(s;x) for systems of arbitrary dimension d when β’=0 and also for d=1 when β’≠0. We also describe new Monte Carlo data for finite Γ, β’=0, and d=1,2. The latter suggests, in particular, the existence of phase transitions for d=1, finite Γ, and some choices for c(s;x).Keywords
This publication has 13 references indexed in Scilit:
- Effective Hamiltonian description of nonequilibrium spin systemsPhysical Review Letters, 1989
- Kinetic phase transitions and tricritical point in an Ising model with competing dynamicsPhysics Letters A, 1987
- Reaction-diffusion equations for interacting particle systemsJournal of Statistical Physics, 1986
- Rigorous Derivation of Reaction-Diffusion Equations with FluctuationsPhysical Review Letters, 1985
- Deterministic limit of the stochastic model of chemical reactions with diffusionAdvances in Applied Probability, 1980
- Strong approximation theorems for density dependent Markov chainsStochastic Processes and their Applications, 1978
- SynergeticsPublished by Springer Science and Business Media LLC ,1978
- Limit theorems for sequences of jump Markov processes approximating ordinary differential processesJournal of Applied Probability, 1971
- Solutions of ordinary differential equations as limits of pure jump markov processesJournal of Applied Probability, 1970
- Time-Dependent Statistics of the Ising ModelJournal of Mathematical Physics, 1963