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The one-dimensional spin-1/2 ANNNI model in non-commuting magnetic fields

URN to cite this document: urn:nbn:de:bvb:703-opus-2370

Title data

Adegoke, Adekunle Moses:
The one-dimensional spin-1/2 ANNNI model in non-commuting magnetic fields.
Bayreuth , 2006
( Doctoral thesis, 2006 , University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

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Abstract

In this thesis we have investigated the one-dimensional spin-1/2 Axial Next Nearest Neighbour Ising (ANNNI) model in non-commuting magnetic fields. As a starting point we obtained an estimate of the phase diagram of the model by treating the spins as classical vectors. This was followed by an investigation of the zero temperature ground state of the one-dimensional spin-1/2 ANNNI model in a longitudinal magnetic field. By using the symmetries of the Hamiltonian, we were able to diagonalize the longitudinal ANNNI model exactly. We found that there are four different possible ground state configurations for the longitudinal ANNNI model, in the thermodynamic limit. Rayleigh Schroedinger perturbation series for the ground state energy of the ANNNI model in non-commuting fields were then developed in each of the four ordered regions. Order parameters and the associated susceptibilities as well as specific heats were calculated. By application of the finite-size scaling technique it was possible to obtain the phase boundaries of the model numerically. For certain limits of the full Hamiltonian we compared the obtained results with the existing literature and we got good agreement.

Abstract in another language

Gegenstand dieser Arbeit war die Untersuchung des eindimensionalen Spin-1/2 Ising Modells mit Uebernaechster - Nachbar Wechselwirkung (das sog. ANNNI Modell) in nichtkommutierenden magnetischen Feldern.Als Ausgangspunkt behandelten wir die Spins als klassische Vektoren um eine Abschaetzung des Phasendiagramms zu erhalten. Diesem folgte eine Untersuchung des T=0 Grundzustandes des eindimensionalen Spin-1/2 ANNNI Modells mit longitudinalem Feld. Durch Ausnutzen der Symmetrieeigenschaften des Hamiltonians, war es moeglich das longitudinale Modell exakt zu diagonalisieren. Wir fanden heraus, dass es im thermodynamischen Limes vier moegliche, voneinander verschiedene Grundzustandskonfigurationen gibt.Dann wurde fuer das ANNNI Modell mit nichtkommutierenden Feldern die Grundzustandsenergie in den vier geordneten Regionen mittels Raleigh Schroedinger Stoerungsentwicklung entwickelt. Sowohl Ordnugsparameter mit zugehoerigen Suszeptibilitaeten als auch spezifische Waermen wurden berechnet. Durch Anwendung der finite-size scaling Technik war es moeglich die Phasengrenzen des Modells numerisch zu erhalten. Fuer gewisse Grenzfaelle des gesamten Hamiltonians wurde ein Vergleich mit Literaturdaten durchgefuehrt und gute Uebereinstimmung erzielt.

Further data

Item Type: Doctoral thesis (No information)
Keywords: Ising-Modell; Spin-einhalb-System; Quantenspinsystem; ANNNI model
DDC Subjects: 500 Science > 530 Physics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-opus-2370
Date Deposited: 25 Apr 2014 12:43
Last Modified: 25 Apr 2014 12:43
URI: https://epub.uni-bayreuth.de/id/eprint/783

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