From steady-state TASEP model with open boundaries to 1D Ising model at negative fugacity

Zn elliptic Gaudin model with open boundaries

The Zn elliptic Gaudin model with integrable boundaries specified by generic nondiagonal K-matrices with n+ 1 free boundary parameters is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. PACS: 03.65.Fd; 04.20.Jb; 05.30.-d; 75.10.Jm

Nonequilibrium Steady State in a Quantum System: One-Dimensional Transverse Ising Model with Energy Current

We study the nonequilibrium steady states of an Ising chain in a transverse field h by investigating the effect of a field l, which drives the current of energy. The zero-temperature, h-l phase diagram is determined exactly, and it is found that the energy current appears continuously above a threshold l . lcshd. The long-range magnetic order (present for h , hc , l , lc) is destroyed in the cu...

Emergent 1d Ising Behavior in an Elementary Cellular Automaton Model

The fundamental nature of an evolving one-dimensional (1D) Ising model is investigated with an elementary cellular automaton (CA) simulation. The emergent CA simulation employs an ensemble of cells in one spatial dimension, each cell capable of two microstates interacting with simple nearest-neighbor rules and incorporating an external field. The behavior of the CA model provides insight into t...

Appendix K Earthworm Fugacity Model

Nonequilibrium steady state of the kinetic Glauber-Ising model under an alternating magnetic field.

When periodically driven by an external magnetic field, a spin system can enter a phase of steady entrained oscillations with nonequilibrium probability distribution function. We consider an arbitrary magnetic field switching its direction with frequency comparable with the spin-flip rate and show that the resulting nonequilibrium probability distribution can be related to the system equilibriu...