Dynamical behavior of the random-bond transverse Ising model with four-spin interactions

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We study the time evolution of the one-dimensional random-bond transverse Ising model with four-spin interactions. We calculate the time-dependent correlation function as well as the longitudinal relaxation function of the infinite chain. We analyze how the presence of disorder affect the dynamical behavior of the system in comparison with the pure model. We find that the main effect of disorder is to produce a crossover from a central mode to a collective-mode type of dynamics, as the concentration of weaker bonds is enhanced. Such crossover is also present in the case of an increase in bond dilution. The role of time evolution of one-dimensional quantum spin systems has been a long-standing theoretical and experimental problem. 1 Among them, the transverse Ising model with multispin interactions, regarded as one of the simplest with a nontrivial dynamics, has attracted considerable interest in recent years. 2,3 On the other hand, the presence of bond randomness has been shown to affect the behavior of magnetic materials in a drastic way providing a very rich area of investigation. In some materials it is present in the form of dilution caused by missing magnetic bonds or sites. In other class of systems it manifests itself through fluctuations in the magnitude of the exchange couplings due to structural disorder, as in glassy materials. Most of the research in disordered systems have been concentrated on obtaining phase diagrams and thermodynamic functions. 3 Much less effort has been made to obtain the dynamical behavior of these systems. Recently, the time evolution of the usual two-body random transverse Ising system was carried out by means of the method of recurrence relations. 4 The crossover from a central