2002/10/24 by B. Schmittmann, F. Schmueser, Frank Schmüser
Mathematics · Physics and Astronomy · #Condensed matter physics #Factorization #Glauber #Ising model #Mathematical physics #Mathematics #Opinion Dynamics and Social Influence #Physics #Quantum many-body systems #Quantum mechanics #Renormalization group #Spins #Stationary state #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.046130
published as Phys. Rev. E 66, 046130 (2002) · 9 pages
openalex publication_date 2002/10/24 · arxiv created 2002/12/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature T(e) (T(o)). Detailed balance is violated so that the spin chain settles into a nonequilibrium stationary state, characterized by multiple interactions of increasing range and spin order. We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state. Two nontrivial amplitudes reflect the sublattice symmetries; otherwise, correlations decay exponentially, modulo the periodicity of the ring. In the long-chain limit, they factorize into products of two-point functions, in precise analogy to the equilibrium Ising chain. The exact solution confirms the expectation, based on simulations and renormalization group arguments, that the long-time, long-distance behavior of this two-temperature model is Ising-like, in spite of the apparent complexity of the stationary distribution.