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Statistical thermodynamics of long-range quantum spin systems
Thesis (MSc)--Stellenbosch University, 2012.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2012
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| _version_ | 1867613834769858560 |
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| access_status_str | Open Access |
| author | Olivier, G. J. F. (Gerrit Jacobus Francois) |
| author2 | Kastner, Michael |
| author_browse | Kastner, Michael Olivier, G. J. F. (Gerrit Jacobus Francois) |
| author_facet | Kastner, Michael Olivier, G. J. F. (Gerrit Jacobus Francois) |
| author_sort | Olivier, G. J. F. (Gerrit Jacobus Francois) |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2012. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/20003 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:42:26.594Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2012 |
| publishDateRange | 2012 |
| publishDateSort | 2012 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/20003 Statistical thermodynamics of long-range quantum spin systems Olivier, G. J. F. (Gerrit Jacobus Francois) Kastner, Michael Stellenbosch University. Faculty of Science. Dept. of Physics. Long-range interactions Spin systems Microcanonical ensemble Entropy functions Dissertations -- Physics Theses -- Physics Non-equivalence of ensembles Thesis (MSc)--Stellenbosch University, 2012. ENGLISH 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. AFRIKAANSE 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. 2012-03-13T11:29:28Z 2012-03-30T10:32:46Z 2012-03-13T11:29:28Z 2012-03-30T10:32:46Z 2012-03 Thesis http://hdl.handle.net/10019.1/20003 en_ZA Stellenbosch University 61 p. : ill. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Long-range interactions Spin systems Microcanonical ensemble Entropy functions Dissertations -- Physics Theses -- Physics Non-equivalence of ensembles Olivier, G. J. F. (Gerrit Jacobus Francois) Statistical thermodynamics of long-range quantum spin systems |
| title | Statistical thermodynamics of long-range quantum spin systems |
| title_full | Statistical thermodynamics of long-range quantum spin systems |
| title_fullStr | Statistical thermodynamics of long-range quantum spin systems |
| title_full_unstemmed | Statistical thermodynamics of long-range quantum spin systems |
| title_short | Statistical thermodynamics of long-range quantum spin systems |
| title_sort | statistical thermodynamics of long range quantum spin systems |
| topic | Long-range interactions Spin systems Microcanonical ensemble Entropy functions Dissertations -- Physics Theses -- Physics Non-equivalence of ensembles |
| url | http://hdl.handle.net/10019.1/20003 |
| work_keys_str_mv | AT oliviergjfgerritjacobusfrancois statisticalthermodynamicsoflongrangequantumspinsystems |