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Statistical thermodynamics of long-range quantum spin systems

dc.contributor.advisorKastner, Michaelen_ZA
dc.contributor.authorOlivier, G. J. F. (Gerrit Jacobus Francois)en_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Physics.en_ZA
dc.date.accessioned2012-03-13T11:29:28Z
dc.date.accessioned2012-03-30T10:32:46Z
dc.date.available2012-03-13T11:29:28Zen_ZA
dc.date.available2012-03-30T10:32:46Z
dc.date.issued2012-03
dc.identifier.urihttp://hdl.handle.net/10019.1/20003
dc.descriptionThesis (MSc)--Stellenbosch University, 2012.en_ZA
dc.description.abstractENGLISH ABSTRACT:In this thesis we discuss some of the anomalies present in systems with long-range interactions, for instance negative specifc heat and negative magnetic susceptibility, and show how they can be related to the convexity properties of the thermodynamic potentials and nonequivalence of ensembles. We also discuss the possibility of engineering long-range quantum spin systems with cold atoms in optical lattices to experimentally verify the existence of nonequivalence of ensembles. We then formulate an expression for the density of states when the energy and magnetisation correspond to a pair of non-commuting operators. Finally we analytically compute the entropy s(;m) as a function of energy, and magnetisation, m, for the anisotropic Heisenberg model with Curie-Weiss type interactions. The results show that the entropy is non-concave in terms of magnetisation under certain circumstances which in turn indicates that the microcanonical and canonical ensembles are not equivalent and that the magnetic susceptibility is negative. After making an appropriate change of variables we show that a second-order phase transition can be present at negative temperatures in the microcanonical ensemble which cannot be represented in the canonical ensemble.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: In hierdie tesis bespreek ons van die onverwagte eienskappe wat sisteme met lang afstand wisselwerkings kan openbaar, byvoorbeeld negatiewe spesi eke warmte en negatiewe magnetiese suseptibiliteit. Ons dui ook die ooreenkoms tussen hierdie gedrag en die konveksiteit van die termodinamiese potensiale en nie-ekwivalente ensembles aan. Hierna bespreek ons die moontlikheid om lang afstand kwantum spin sisteme te realiseer met koue atome in 'n optiese rooster. Daarna wys ons hoe dit moontlik is om 'n uitdrukking vir die digtheid van toestande te formuleer vir sisteme waar die energie en magnetisasie ooreenstem met operatore wat nie met mekaar kommuteer nie. Uiteindelik bepaal ons die entropie, s( ;m), in terme van die energie, , en magnetisasie, m, vir die anisotropiese Heisenberg model met Curie-Weiss tipe interaksies. Die resultate wys dat die entropie onder sekere omstandighede nie konkaaf in terme van magnetisasie is nie. Dit, op sy beurt, dui aan dat die mikrokanoniese en kanoniese ensembles nie ekwivalent is nie en dat die magnetiese suseptibiliteit negatief kan wees. Nadat ons 'n toepaslike transformasie van veranderlikes maak, wys ons dat 'n tweede orde fase-oorgang by negatiewe temperature kan plaasvind in die mikrokanoniese ensemble wat nie verteenwoordig kan word in die kanoniese ensemble nie.af_ZA
dc.format.extent61 p. : ill.
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.subjectLong-range interactionsen_ZA
dc.subjectSpin systemsen_ZA
dc.subjectMicrocanonical ensembleen_ZA
dc.subjectEntropy functionsen_ZA
dc.subjectDissertations -- Physicsen_ZA
dc.subjectTheses -- Physicsen_ZA
dc.subjectNon-equivalence of ensemblesen_ZA
dc.titleStatistical thermodynamics of long-range quantum spin systemsen_ZA
dc.typeThesis
dc.rights.holderStellenbosch University


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