Dynamics of the one-dimensional random transverse Ising model with next-nearest-neighbor interactions

TL;DR

This study investigates the high-temperature dynamics of a one-dimensional disordered transverse Ising model with both nearest and next-nearest neighbor interactions, revealing how disorder type and interaction strength influence dynamic behavior.

Contribution

It provides the first detailed analysis of how NNN interactions and disorder types affect the dynamical properties of the disordered transverse Ising model.

Findings

Crossover from collective-mode to central-peak behavior with increasing disorder strength.

Dynamics become more complex with Gaussian disorder.

Central-peak behavior intensifies as NNN interactions increase, especially beyond half the NN interaction strength.

Abstract

The dynamics of the one-dimensional random transverse Ising model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions is studied in the high-temperature limit by the method of recurrence relations. Both the time-dependent transverse correlation function and the corresponding spectral density are calculated for two typical disordered states. We find that for the bimodal disorder the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one and for the Gaussian disorder the dynamics is complex. For both cases, it is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as $K_{i}$ increase, especially when $K_{i}>J_{i}/2$ ($J_{i}$ and $K_{i}$ are exchange couplings of the NN and NNN interactions, respectively). However, the effects are small when the NNN interactions are weak ($K_{i}<J_{i}/2$).