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Previous issue date: 2000-01-14 / In this work we have studied the effects of random biquadratic and random fields in spin-glass models using the replica method.
The effect of a random biquadratic coupling was studied in two spin-1 spin-glass models: in one case the interactions occur between pairs of spins, whereas in the second one the interactions occur between p spins and the limit p > oo is considered. Both couplings (spin glass and biquadratic) have zero-mean Gaussian probability distributions. In the first model, the replica-symmetric assumption reveals that the system presents two pha?ses, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic cou?plings between the spins. For the case p oo, the replica-symmetric assumption yields again only two phases, namely, paramagnetic and quadrupolar. In both these phases the spin-glass parameter is zero. Besides, it is shown that they are stable under the Almeida-Thouless stability analysis. One of them presents negative entropy at low temperatures. We developed one step of replica simmetry breaking and noticed that a new phase, the biquadratic glass phase, emerge. In this way we have obtained the correct phase diagram, with.three first-order transition lines. These lines merges in a common triple point.
The effects of random fields were studied in the Sherrington-Kirkpatrick model consi?dered in the presence of an external random magnetic field following a trimodal distribu?tion {P{hi) = p+S(hi - h0) +Po${hi) +pS(hi + h0))- It is shown that the border of the ferromagnetic phase may present, for conveniently chosen values of p0 and hQ, first-order phase transitions, as well as tricritical points at finite temperatures. It is verified that the first-order phase transitions are directly related to the dilution in the fields: the extensions of these transitions are reduced for increasing values of po- In fact, the threshold value pg, above which all phase transitions are continuous, is calculated analytically. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified / Nesse trabalho estudamos os efeitos de acoplamentos biquadr?ticos e campos aleat?rios em vidros de spins utilizando o m?todo das r?plicas.
O efeito do acoplamento biquadr?tico aleat?rio ? estudado em um vidro de spins com spin 1 em duas situa??es diferentes: no caso onde as intera??es s?o entre pares de spins e no caso onde a intera??o ocorre entre p spins no limite p > oo. Ambos os acoplamen?tos (vidro de spins e biquadr?tico) t?m distribui??o de probabilidades gaussianas com m?dia zero. Para intera??es entre pares de spins a solu??o com simetria entre r?plicas fornece as fases paramagn?tica e vidro de spins separadas por uma linha de transi??es cont?nuas. A an?lise de estabilidade da solu??o com simetria entre r?plicas fornece, al?m da instabilidade usual associada com o ordenamento vidro de spins, uma nova fase devido ao acoplamento biquadr?tico entre os spins. Para o caso p = oo, a solu??o com simetria entre r?plicas fornece apenas duas fases, marginalmente est?veis com rela??o ? an?lise de estabilidade de de Almeida e Thouless. Entretanto, uma dessas fases apresenta entropia negativa a baixas temperaturas. Implementamos tamb?m um passo de quebra de sime?tria nos par?metros vidros de spins e vidro quadrupolar e obtivemos o diagrama de fases correto, incluindo a fase vidro de spins. Nesse caso, todas as transi??es s?o de primeira ordem e as tr?s fases coexistem em um ponto triplo.
Os efeitos de campos aleat?rios s?o estudados no modelo de Sherrington-Kirkpatrick, onde consideramos um campo aleat?rio com distribui??o de probabilidades trimodal {P(hi) = p+?(hi - h0) +po?(h0) +p-6(hi + ho))- Mostramos que para valores convenientes de po e h0, a fronteira ferromagn?tica pode apresentar transi??es de primeira ordem e pontos tricr?ticos a temperaturas finitas. Verificamos que as transi??es de primeira ordem est?o diretamente relacionadas com a dilui??o do campo: as extens?es dessas transi??es s?o reduzidas quando aumentamos o valor de po- De fato, o valor pl acima do qual todas as transi??es s?o cont?nuas ? calculado analiticamente. Fizemos tamb?m a an?lise de es?tabilidade da solu??o com simetria entre r?plicas e determinamos as regi?es de validade desta solu??o
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/16591 |
| Date | 14 January 2000 |
| Creators | Ara?jo, Jo?o Medeiros de |
| Contributors | CPF:27023320482, http://lattes.cnpq.br/5307397723573993, Mariz, Ananias Monteiro, CPF:07136200482, http://lattes.cnpq.br/7218040405934056, Nobre, Fernando Dantas, CPF:13068164400, http://lattes.cnpq.br/2007917360087831, Yokoi, Carlos Seihiti Orii, CPF:00353196827, http://lattes.cnpq.br/5162520733303284, Almeida, Jairo Rolim Lopes de, CPF:05451230463, http://lattes.cnpq.br/7284089296377200, Costa, Francisco Alexandre da |
| Publisher | Universidade Federal do Rio Grande do Norte, Programa de P?s-Gradua??o em F?sica, UFRN, BR, F?sica da Mat?ria Condensada; Astrof?sica e Cosmologia; F?sica da Ionosfera |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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