https://doi.org/10.1140/e10051-002-0007-9
Kink solutions of the classical transverse field Ising chain
Technische Universität München,
Zentrum Mathematik, 80290 München, Germany
Corresponding author: a johann@mathematik.tu-muenchen.de
Received:
23
February
2001
Revised:
4
October
2001
Published online: 15 January 2002
We investigate stationary and travelling wave solutions of the classical
one-dimensional transverse field Ising model. Results are given on the
existence, shape and stability of kink solutions and periodic solutions.
We review recent analytical results (e.g., the proof of existence of a
one-parameter family of stationary kink solutions and the proof of existence
of travelling wave kink solutions with nonzero velocity 
) and
extend them by the use of numerical methods. Small oscillations arising in the
tails of travelling kink solutions are investigated numerically. In the end,
stability analysis puts some light on pinning effects.
PACS: 05.45.Yv – Solitons / 75.10.Hk – Classical spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
