One-Dimensional Time-Dependent Ising Model in an External Magnetic Field

The relaxation process, through which the inequilibrium state described by the Ising model reaches the equilibrium state, was proposed. The process is defined by the action of the transition matrix on the vector of state and the demand of its normalisation. It is assumed that in the state of inequilibrium the vector of state has the same functional dependence as the eigenvector of the transition matrix corresponding to the highest eigenvalue. Two cases are considered: when the cell under transformation is composed of one or two sites. The calculations were performed for a uniform initial state. For the two cases of one and two-site cells the modes of reaching the equilibrium state via magnetisation were compared. When the external magnetic field and temperature tend to zero, both magnetisation and the correlation function of the nearest neighbours show the critical slowing down phenomenon.