Spin-1/2 Ising ladder with randomly coupled rung interaction and transverse magnetic field

The quantum spin-1/2 Ising ladder with homogeneous side rail interaction and disordered rung interaction in the presence of a random site transverse magnetic field has been studied using the method of recurrence relations in the high-temperature limit. The first six recurrants have been exactly calculated, and a linear extrapolation process has been used to obtain a total of 100 recurrants. This extrapolation allows us to extend the analysis to longer times. Both the rung coupling and the transverse field obey a bimodal distribution. The time autocorrelation functions of the z-component dynamic spin variable have been obtained. We have considered several cases of rung and transverse field distributions, as well as several values of the Hamiltonian parameters. The results show that the disorder present in the rung interaction and external transverse field affects the behavior of the temporal autocorrelation and the spectral functions in all studied cases. In addition, the interesting case where the rung interactions and the transverse magnetic field are correlated has also been studied. In general, transition in the dynamics of the system from individual to collective mode was observed depending on the dominant kind of interaction in the sites, that is, whether most of the sites were subject to a strong external field or strong interchain local interactions.