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

J. J. Luque, A. Córdoba

M. Błaszyk

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.

W. S. Lo, Robert A. Pelcovits

We report the results of Monte Carlo simulations on a two-dimensional Ising model in a sinusoidally oscillating external magnetic field. We find evidence for a dynamical phase transition, supporting the results of recent mean-field and large-N analyses of this model. We also analyze the hysteresis loops as a function of the amplitude and frequency of the applied field, fitting our data to a proposed areal scaling law.

Kyozi Kawasaki, Tomoji Yamada

Erol Vatansever, Ümit Akıncı, Hamza Polat

Kunle Adegoke, Henry Otobrise, Tolulope Famoroti +3 more

We give an explicit matrix representation for the Hamiltonian of the Ising model in mutually orthogonal external magnetic fields, using as basis the eigenstates of a system of non-interacting spin~$1/2$ particles in external magnetic fields. We subsequently apply our results to obtain an analytical expression for the ground state energy per spin, to the fourth order in the exchange integral, for the Ising model in perpendicular external fields.