Made available in DSpace on 2014-06-12T18:01:16Z (GMT). No. of bitstreams: 2 arquivo2349_1.pdf: 1245146 bytes, checksum: 48f142847a52a8ed12ebbda5b224106b (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, calculamos a razão entre as amplitudes da susceptibilidade acima e abaixo da temperatura crítica associada ao ponto de Lifshitz m-axial. Obtemos resultados até primeira ordem na expansão no número de loops. Mostramos que o valor da razão entre as amplitudes para o caso anisotrópico generaliza o resultado conhecido para o caso m = 1. A razão para o caso isotrópico foi obtida pela primeira vez. Os resultados obtidos são universais

No description available.

No description available.

Experimentally pure Lifshitz critical behavior has only been reported in the orthorhombic magnetic system MnP which exhibits uniaxial Ising-Type Lifshitz points LP (d=3, n=l, m=l). Two LPs have been previously identified in MnP. One when the external magnetic field H was applied along the intermediate b axis, the other when IH was along the hard anisotropy axis a. Both LPs occurs roughly at the same temperature (TL ~121K) but at different values of H due to the difference in anisotropy. In this work we report on measurements made with H applied within the ab plane. Two configurations were studied: (1) with H making an angle of 20° with the b axis and (2) with H at 45° in the b (and a) axis. The observed phase diagram obtained using an AC susceptibility technique shows, near the confluence of the modulated and ferromagnetic phases with the paramagnetic phase, the same characteristics of the phase boundaries found when H is along a and also along b . The temperature at the multicritical point is TL~120K. From an analysis of the shape of the phase boundaries near TL we obtained a crossover exponent =0.61±0.02, a value that is consistent with the found for IH along the a and the b axis. This value is also consistent with the predicted theoretically from Renormalization-Group calculation. These data suggest that there is a line of LPs connecting the multicritical points found when H is along the b and a axis. / Experimentally pure Lifshitz critical behavior has only been reported in the orthorhombic magnetic system MnP which exhibits uniaxial Ising-Type Lifshitz points LP (d=3, n=l, m=l). Two LPs have been previously identified in MnP. One when the external magnetic field H was applied along the intermediate b axis, the other when IH was along the hard anisotropy axis a. Both LPs occurs roughly at the same temperature (TL ~121K) but at different values of H due to the difference in anisotropy. In this work we report on measurements made with H applied within the ab plane. Two configurations were studied: (1) with H making an angle of 20° with the b axis and (2) with H at 45° in the b (and a) axis. The observed phase diagram obtained using an AC susceptibility technique shows, near the confluence of the modulated and ferromagnetic phases with the paramagnetic phase, the same characteristics of the phase boundaries found when H is along a and also along b . The temperature at the multicritical point is TL~120K. From an analysis of the shape of the phase boundaries near TL we obtained a crossover exponent =0.61±0.02, a value that is consistent with the found for IH along the a and the b axis. This value is also consistent with the predicted theoretically from Renormalization-Group calculation. These data suggest that there is a line of LPs connecting the multicritical points found when H is along the b and a axis.

Experimentally pure Lifshitz critical behavior has only been reported in the orthorhombic magnetic system MnP which exhibits uniaxial Ising-Type Lifshitz points LP (d=3, n=l, m=l). Two LPs have been previously identified in MnP. One when the external magnetic field H was applied along the intermediate b axis, the other when IH was along the hard anisotropy axis a. Both LPs occurs roughly at the same temperature (TL ~121K) but at different values of H due to the difference in anisotropy. In this work we report on measurements made with H applied within the ab plane. Two configurations were studied: (1) with H making an angle of 20° with the b axis and (2) with H at 45° in the b (and a) axis. The observed phase diagram obtained using an AC susceptibility technique shows, near the confluence of the modulated and ferromagnetic phases with the paramagnetic phase, the same characteristics of the phase boundaries found when H is along a and also along b . The temperature at the multicritical point is TL~120K. From an analysis of the shape of the phase boundaries near TL we obtained a crossover exponent =0.61±0.02, a value that is consistent with the found for IH along the a and the b axis. This value is also consistent with the predicted theoretically from Renormalization-Group calculation. These data suggest that there is a line of LPs connecting the multicritical points found when H is along the b and a axis. / Experimentally pure Lifshitz critical behavior has only been reported in the orthorhombic magnetic system MnP which exhibits uniaxial Ising-Type Lifshitz points LP (d=3, n=l, m=l). Two LPs have been previously identified in MnP. One when the external magnetic field H was applied along the intermediate b axis, the other when IH was along the hard anisotropy axis a. Both LPs occurs roughly at the same temperature (TL ~121K) but at different values of H due to the difference in anisotropy. In this work we report on measurements made with H applied within the ab plane. Two configurations were studied: (1) with H making an angle of 20° with the b axis and (2) with H at 45° in the b (and a) axis. The observed phase diagram obtained using an AC susceptibility technique shows, near the confluence of the modulated and ferromagnetic phases with the paramagnetic phase, the same characteristics of the phase boundaries found when H is along a and also along b . The temperature at the multicritical point is TL~120K. From an analysis of the shape of the phase boundaries near TL we obtained a crossover exponent =0.61±0.02, a value that is consistent with the found for IH along the a and the b axis. This value is also consistent with the predicted theoretically from Renormalization-Group calculation. These data suggest that there is a line of LPs connecting the multicritical points found when H is along the b and a axis.

There are two main tools for determining the stability of nonlinear partial differential equations (PDEs): Lyapunov Theory and linearization. The former has the advantage of providing stability results for nonlinear equations directly, while the latter considers the stability of linear equations and then further justification is needed to show the linear stability implies local stability of the nonlinear equation. Linearization has the advantage of investigating stability on a simpler equation; however, the justification can be difficult to prove. Both Lyapunov Theory and linearization are applied to the Landau--Lifshitz equation, a nonlinear PDE that describes the behaviour of magnetization inside a magnetic object. It is known that the Landau-Lifshitz equation has an infinite number of stable equilibrium points. We present a control that forces the system from one equilibrium to another. This is proved using Lyapunov Theory. The linear Landau--Lifshitz equation is also investigated because it provides insight to the nonlinear equation. The linear model is shown to be well--posed and its eigenvalue problem is solved. The resulting eigenvalues suggest an appropriate control for the nonlinear Landau--Lifshitz equation. Mathematically, the control causes the initial equilibrium to no longer be an equilibrium and the second point to be an asymptotically stable equilibrium point. This implies the magnetization has moved to the second equilibrium and hence the control objective is successfully achieved. The existence of multiple stable equilibria is closely related to hysteresis. This is a phenomenon that is often characterized by a looping behaviour; however, the existence of a loop is not sufficient to identify hysteretic systems. A more precise definition is required, which is presented, and applied to the Landau--Lifshitz equation (both linear and nonlinear) to establish the presence of hysteresis.

Submitted by Danielle Karla Martins Silva (danielle.martins@ufpe.br) on 2015-03-06T14:20:34Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Borba-Tese.pdf: 1333179 bytes, checksum: 96c554cc5271892d1ae4d75b520d7c24 (MD5) / Made available in DSpace on 2015-03-06T14:20:34Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Borba-Tese.pdf: 1333179 bytes, checksum: 96c554cc5271892d1ae4d75b520d7c24 (MD5) Previous issue date: 2012 / CNPq; FACEPE / Atrav es da utiliza c~ao de uma teoria de campo escalar representada no espa co dos momentos, vamos estudar os efeitos do tamanho nito no comportamento cr tico de sistemas competitivos m-axiais com d dimens~oes em uma geometria cujas superf cies delimitadoras s~ao placas planas e paralelas. Tais placas s~ao de extens~ao in nita e s~ao separadas por uma dist^ancia L. O par^ametro de ordem estar a sujeito a condi c~oes de contorno peri odicas ou antiperi odicas ao longo das duas superf cies. Ambas as formula c~oes com campos massivos e n~ao-massivos ser~ao aplicadas a m de obter os expoentes cr ticos respectivamente nos limites de escalamento ultravioleta e infravermelho, que s~ao necess arios a descri c~ao das regi~oes de escala presentes em sistemas com tamanho nito. Come caremos analisando sistemas sem competi c~ao (m = 0). Vamos introduzir uma nova descri c~ao para os regimes de \crossover" dimensional usuais relacionados com as regi~oes de escala. Desde que evitemos esse \crossover", caracterizado apenas por valores pequenos de L, calcularemos os expoentes e perturbativamente at e as respectivas ordens de dois e tr^es loops e veremos que eles s~ao id^enticos aos de um sistema in nito (L ! 1). Em seguida, vamos estender o nosso m etodo de an alise do tamanho nito para sistemas competitivos m-axiais no ponto cr tico de Lifshitz. Em uma abordagem inicial, consideraremos nita uma das dire c~oes ao longo do subespa co sem competi c~ao e observaremos um comportamento semelhante com rela c~ao ao \crossover" dimensional de sistemas n~ao-competitivos. Para L su cientemente grande, calcularemos os expoentes cr ticos L2, L2, L4 e L4 at e ordens de pelo menos dois loops com aux lio de uma aproxima c~ao especial para a regulariza c~ao das integrais de Feynman. Tais expoentes ser~ao id^enticos aos do sistema in nito. O pr oximo passo consiste em tornar nita a dire c~ao ao longo do eixo de competi c~ao em um sistema uniaxial (m = 1). Utilizaremos nessa con gura c~ao uma nova representa c~ao para as integrais de Feynman e, evitando a regi~ao de \crossover", calcularemos de forma exata at e ordens de dois loops os expoentes L2 e L2. Os nossos resultados ser~ao comparados com os expoentes obtidos por m etodos aproximados e por simula c~oes de Monte Carlo presentes na literatura.

Dois modelos descrevendo sistemas magnéticos modulados são estudados na presença de um campo magnético. Na primeira parte consideramos um modelo de Ising com interações competitivas numa única direção espacial (modelo ANNNI). A superfície crítica, a linha tricrítica, a estrutura das fases moduladas, e os diagramas de fases são determinados na aproximação de campo médio. O comportamento crítico e tricrítico é analisado através do método de Grupo de Renormalização. Na segunda parte estudamos um modelo adequado à descrição do composto MnP. Cálculos realizados na aproximação de campo médio e através do método de Grupo de Renormalização contribuem para esclarecer os resultados experimentais acerca do ponto de Lifshitz observado neste composto. / Two models describing modulated magnetic systems are studied in the presence of a magnetic field. The first part is dedicated to the study of an Ising model with competing interactions along one of the spatial directions (ANNNI model). The critical surface, the tricritical line, the structure of the modulated phases, and the phase diagrams are determined in the mean field approximation. The critical and the tricritical behaviour is analised by the Renormalization Group method. The second part is concerned with a model suitable for the description of the compound MnP. Calculations carried out in the mean field approximation and through the Renormalization Group method provide a better understanding of the experimental results on the Lifshitz point observed in this compound.

Dois modelos descrevendo sistemas magnéticos modulados são estudados na presença de um campo magnético. Na primeira parte consideramos um modelo de Ising com interações competitivas numa única direção espacial (modelo ANNNI). A superfície crítica, a linha tricrítica, a estrutura das fases moduladas, e os diagramas de fases são determinados na aproximação de campo médio. O comportamento crítico e tricrítico é analisado através do método de Grupo de Renormalização. Na segunda parte estudamos um modelo adequado à descrição do composto MnP. Cálculos realizados na aproximação de campo médio e através do método de Grupo de Renormalização contribuem para esclarecer os resultados experimentais acerca do ponto de Lifshitz observado neste composto. / Two models describing modulated magnetic systems are studied in the presence of a magnetic field. The first part is dedicated to the study of an Ising model with competing interactions along one of the spatial directions (ANNNI model). The critical surface, the tricritical line, the structure of the modulated phases, and the phase diagrams are determined in the mean field approximation. The critical and the tricritical behaviour is analised by the Renormalization Group method. The second part is concerned with a model suitable for the description of the compound MnP. Calculations carried out in the mean field approximation and through the Renormalization Group method provide a better understanding of the experimental results on the Lifshitz point observed in this compound.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-10T19:33:25Z No. of bitstreams: 1 EDME VALE PEREIRA – DISSERTAÇÃO (PPGFísica) 2016.pdf: 765741 bytes, checksum: 06e478d901631d57a3c3905fb212d89c (MD5) / Made available in DSpace on 2018-10-10T19:33:25Z (GMT). No. of bitstreams: 1 EDME VALE PEREIRA – DISSERTAÇÃO (PPGFísica) 2016.pdf: 765741 bytes, checksum: 06e478d901631d57a3c3905fb212d89c (MD5) Previous issue date: 2016-08-11 / Capes / Neste trabalho, estudamos um escalonamento de Horava-Lifshitz destinado a reescrever uma eletrodinâmica que viola a invariância de Lorentz com operadores derivativos controlados por um quadrivetor constante n . Esse método foi usado inicialmente para escalonar a lagrangiana de Maxwell e depois a lagrangiana de altas ordens derivativas, conhecida como modelo Myers-Pospelov. Após o processo de escalonamento, obtivemos que ambas as lagrangianas são descritas em função de um expoente crítico z, que insere um caráter anisotrópico para ambas as teorias. Foram obtidos os propagadores de Feynman e as relações de dispersão para ambos os modelos. Devido ao caráter irrefringente atribuído ao modelo de altas ordens derivativas, usamos os modos de propagação associados, como as soluções por frequências, e efetuamos os cálculos de polarização para determinar os limites superiores de ocorrências dos efeitos da quebra da invariância de Lorentz. Tais operações estão de acordo com as observações de explosões de raios gama, mais especificamente, o evento GRB051218A. O parâmetro que controla a quebra da invariância de Lorentz, apresenta-se superior em 8 (oito) ordens de magnitude, se comparado com alguns resultados da literatura. O atraso temporal na propagação de dois fótons também foi determinado. / In this work, we study a Horava-Lifshitz scaling which can be used to rewrite an electrodynamics which breaks the Lorentz invariance with derivatives operators controlled by a constant four-vector, n . This method was initially used to scale the Maxwell lagrangian and then the high orders derivatives lagrangian, known as Myers-Pospelov model. After of the process, we obtained that both the lagrangian are described in terms of a critical exponent z, which can be inserted as anisotropic character for both theories. The of Feynman propagators and dispersion relations for both models were obtained. Due to the birefringent character attributed to Myers-Pospelov model, we use the associate propagation modes, as solutions for frequencies, and we perform the polarization calculations to determine the upper limits of occurrences related with e ects of Lorentz invariance breaking. Such operations are consistent with the recent observations of gamma-ray bursts, more speci cally, the GRB 051218A event. The parameter which controls of the Lorentz invariance violation, it presents superior in eight (8) orders of magnitude, compared with some results of literature. The time delay in the propagation of two photons was also determined.