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The European Physical Journal B

Kink solutions of the classical transverse field Ising chain

Andreas Johann

Published Jan 1, 2002• 3 citations
Publisher
DOI
10.1140/e10051-002-0007-9

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Dynamics and statistical mechanics of kinks in one-dimensional classical Ising model in a transverse field is studied in a dilute kink-gas approximation along the line with the theory of Krumhansl and Schrieffer. The energy of a single kink is written in a simple analytic form by approximating an exact one-kink solution. Kinks in the system are then treated as gas of quasi-particles. It is shown that the partition function so obtained is coincident with that of the result obtained previously by using the transfermatrix method. The dynamical structure of the system is also calculated to show the existence of central peak due to kink excitations.
We consider the time evolution of two-point correlation function in the transverse-field Ising chain (TFIC) with ring frustration. The time-evolution procedure we investigated is equivalent to a quench process in which the system is initially prepared in a classical kink state and evolves according to the time-dependent Schrödinger equation. Within a framework of perturbative theory (PT) in the strong kink phase, the evolution of the correlation function is disclosed to demonstrate a qualitatively new behavior in contrast to the traditional case without ring frustration.
The influence of phonon fluctuations on the dynamics of kink-like domain-wall excitations in the one-dimensional Ising model with a transverse field (s=1/2) was investigated. It was found that such non-linear excitations behave almost like classical Brownian particles. This is the consequence of the emission and absorption of acoustic phonons excited by domain walls propagating through the vibrating lattice. The effective friction and diffusion constants are also evaluated. It was established that the overall process has the character of Cherenkov-type radiation.