Dipolar interaction and critical dynamics for the transverse Ising model

Abstract

The spectral characteristics of the spin fluctuations of the transverse Ising model (in relation to order-disorder ferroelectrics) are studied beyond the random-phase approximation in terms of an interaction made of both nearest-neighbor and dipole-dipole contributions. Numerical results obtained for high temperature show how the shift and width of the soft mode vary with the dipolar interaction strength. Plots of correlation and relaxation functions are obtained and especially analyzed in the critical region. The critical dynamical properties of the model exhibit a marked $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ anisotropy: as $T\ensuremath{\rightarrow}{T}_{c}^{+}$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ensuremath{\rightarrow}0$ the longitudinal relaxation function ${F}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}^{\mathrm{zz}}(\ensuremath{\omega})$ presents a triple-peak structure (for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ nonperpendicular to the $z$ axis) This feature, due to the dipolar nature of the interaction, finds a place in the context of the central-peak problem.