Dynamical phase transition in one-dimensional kinetic Ising model with nonuniform coupling constants

TL;DR

This paper investigates a one-dimensional kinetic Ising model with nonuniform couplings, revealing a dynamical phase transition characterized by a change in relaxation behavior and boundary rate sensitivity.

Contribution

It extends the kinetic Ising model to include nonuniform couplings and identifies conditions for dynamical phase transitions using transfer matrix methods.

Findings

Existence of fast and slow dynamical phases.

Relaxation time can be independent of boundary reaction rates.

A continuous change in boundary rates causes a non-smooth change in relaxation time.

Abstract

An extension of the Kinetic Ising model with nonuniform coupling constants on a one-dimensional lattice with boundaries is investigated, and the relaxation of such a system towards its equilibrium is studied. Using a transfer matrix method, it is shown that there are cases where the system exhibits a dynamical phase transition. There may be two phases, the fast phase and the slow phase. For some region of the parameter space, the relaxation time is independent of the reaction rates at the boundaries. Changing continuously the reaction rates at the boundaries, however, there is a point where the relaxation times begins changing, as a continuous (nonconstant) function of the reaction rates at the boundaries, so that at this point there is a jump in the derivative of the relaxation time with respect to the reaction rates at the boundaries.