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.

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.

<p>In this thesis I present three publications about the use of<br />valence bonds to gain information about quantum spin systems.<br />Valence bonds are an essential ingredient of low energy states present<br />in many compounds.<br /><br />The first part of this thesis is dedicated to<br />two studies of the antiferromagnetic J₁-J₂ chain with<br />S=1/2. We show how automated variational calculations based on<br />valence bond states can be performed close to the Majumdar-Ghosh point<br />(MG-point). At this point, the groundstate is a product state of<br />dimers (valence bonds between nearest neighbours). In the dimerized<br />region surrounding the MG-point, we find such variational computations<br />to be reliable.<br /><br />The first publication is about<br />the entanglement properties of an impurity attached to the chain. We show<br />how to use the variational method to calculate the negativity, an<br />entanglement measure between the impurity and a distant part of the<br />chain. We find that increasing the impurity coupling and a<br />minute explicit dimerization, suppress the long-ranged entanglement<br />present in the system for small impurity coupling at the MG-point. <br /><br />The second publication is about a<br />transition from commensurate to incommensurate behaviour and how its<br />characteristics depend on the parity of the length of the chain. The<br />variational technique is used in a parameter regime inaccessible to<br />DMRG. We find that in odd chains, unlike in even chains, a very<br />intricate and interesting pattern of level crossings can be observed. <br /><br />The publication of the second part is about novel worm algorithms for<br />a popular quantum Monte Carlo method called valence bond quantum Monte<br />Carlo (VBQMC). The algorithms are based on the notion of a worm<br />moving through a decision tree. VBQMC is entirely formulated in<br />terms of valence bonds. In this thesis, I explain how the approach<br />of VBQMC can be translated to the S_z-basis. The algorithms explained<br />in the publication can be applied to this S_z-method.</p> / Doctor of Philosophy (PhD)