Spin dynamics of random Ising chain in coexisting transverse and longitudinal magnetic fields

The dynamics of the random Ising spin chain in coexisting transverse and longitudinal magnetic fields is studied by the recursion method. Both the spin autocorrelation function and its spectral density are investigated by numerical calculations. It is found that system’s dynamical behaviors depend on the deviation σ J of the random exchange coupling between nearest-neighbor spins and the ratio r l t of the longitudinal and the transverse fields: (i) For r l t = 0 , the system undergoes two crossovers from N independent spins precessing about the transverse magnetic field to a collective-mode behavior, and then to a central-peak behavior as σ J increases. (ii) For r l t ≠ 0 , the system may exhibit a coexistence behavior of a collective-mode one and a central-peak one. When σ J is small (or large enough), system undergoes a crossover from a coexistence behavior (or a disordered behavior) to a central-peak behavior as r l t increases. (iii) Increasing σ J depresses effects of both the transverse and the longitudinal magnetic fields. (iv) Quantum random Ising chain in coexisting magnetic fields may exhibit under-damping and critical-damping characteristics simultaneously. These results indicate that changing the external magnetic fields may control and manipulate the dynamics of the random Ising chain.