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We study the zero temperature quenching dynamics of various extensions of thetransverse Ising model (TIM) when the transverse field is linearly quenchedfrom $-\infty$ to $+\infty$ (or zero) at a finite and uniform rate. The rate ofquenching is dictated by a characteristic scale given by $\tau$. The density ofkinks produced in these extended models while crossing the quantum criticalpoints during the quenching process is calculated using a many bodygeneralization of the Landau-Zener transition theory. The density of kinks inthe final state is found to decay as $\tau^{-1/2}$. In the first modelconsidered here, the transverse Ising Hamiltonian includes an additionalferromagnetic three spin interaction term of strength $J_3$. For $J_3<0.5$, thekink density is found to increase monotonically with $J_3$ whereas it decreaseswith $J_3$ for $J_3>0.5$. The point $J_3=0.5$ and the transverse field$h=-0.5$is multicritical where the density shows a slower decay given by$\tau^{-1/6}$. We also study the effect of ferromagnetic or antiferromagneticnext nearest neighbor (NNN) interactions on the dynamics of TIM under the samequenching scheme. In a mean field approximation, the transverse IsingHamiltonians with NNN interactions are identical to the three spin Hamiltonian.The NNN interactions non-trivially modifies the dynamical behavior, for examplean antiferromagnetic NNN interactions results to a larger number of kinks inthe final state in comparison to the case when the NNN interaction isferromagnetic.

The effect of the three-spin interaction and the next nearest neighbor interaction on the quenching dynamics of a transverse Ising model