The effect of the three-spin interaction and the next-nearest neighbor interaction on the quenching dynamics of a transverse Ising model
| dc.creator | Divakaran, Uma | |
| dc.creator | Dutta, Amit | |
| dc.date | 2008-01-17 | |
| dc.date.accessioned | 2026-07-07T08:54:58Z | |
| dc.date.available | 2026-07-07T08:54:58Z | |
| dc.description | We study the zero temperature quenching dynamics of various extensions of the transverse Ising model (TIM) when the transverse field is linearly quenched from $-\infty$ to $+\infty$ (or zero) at a finite and uniform rate. The rate of quenching is dictated by a characteristic scale given by $τ$. The density of kinks produced in these extended models while crossing the quantum critical points during the quenching process is calculated using a many body generalization of the Landau-Zener transition theory. The density of kinks in the final state is found to decay as $τ^{-1/2}$. In the first model considered here, the transverse Ising Hamiltonian includes an additional ferromagnetic three spin interaction term of strength $J_3$. For $J_3<0.5$, the kink density is found to increase monotonically with $J_3$ whereas it decreases with $J_3$ 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 $τ^{-1/6}$. We also study the effect of ferromagnetic or antiferromagnetic next nearest neighbor (NNN) interactions on the dynamics of TIM under the same quenching scheme. In a mean field approximation, the transverse Ising Hamiltonians with NNN interactions are identical to the three spin Hamiltonian. The NNN interactions non-trivially modifies the dynamical behavior, for example an antiferromagnetic NNN interactions results to a larger number of kinks in the final state in comparison to the case when the NNN interaction is ferromagnetic. | |
| dc.description | 7 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0801.2621 | |
| dc.identifier | http://arxiv.org/abs/0801.2621 | |
| dc.identifier | J. Stat. Mech. (2007) P11001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146132 | |
| dc.subject | Statistical Mechanics | |
| dc.title | The effect of the three-spin interaction and the next-nearest neighbor interaction on the quenching dynamics of a transverse Ising model | |
| dc.type | text |