A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even ͑odd͒ 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 longtime, long-distance behavior of this two-temperature model is Ising-like, in spite of the apparent complexity of the stationary distribution.

By data analysis the ordinary differential equation for the description of an experimental electric resonance circuit with nonlinear capacitor is derived. Triglycine sulfate (TGS) was used as nonlinear dielectric material. This is the most thoroughly investigated ferroelectric with a second order phase transition. Its static dielectric small signal behavior is well described in the framework of the Landau theory, yielding a Duffing-type ordinary differential equation as a model equation of the circuit. Data analysis allows us to check carefully the validity of this model and to determine required corrections of this simplified equation. (c) 1998 American Institute of Physics.

A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature Te (To). Spin flips occur with Glauber-type rates generalised to the case of two temperatures. Driven by the temperature differential, the spin chain settles into a non-equilibrium steady state which corresponds to the stationary solution of a master equation. We construct a perturbation expansion of this master equation in terms of the temperature difference and compute explicitly the first two corrections to the equilibrium Boltzmann distribution. The key result is the emergence of additional spin operators in the steady state, increasing in spatial range and order of spin products. We comment on the violation of detailed balance and entropy production in the steady state.

A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity to a symmetry breaking bifurcation point. In parameter space four phases with different ergodic behaviour are observed. Although the coupling in the map lattice is diffusive, antiferromagnetic ordering is predominant. Via coarse graining the deterministic model is mapped to a master equation which establishes an equivalence between our system and a kinetic Ising model. Such an approach sheds some light on the dependence of the transient behaviour on the system size and the nature of the phase transitions.