O presente trabalho estuda o modelo de Blume-Capel na rede aleatória e também analisa a inclusão de um termo de campo cristalino aleatório e de um termo de campo local aleatório. Ao resolver o modelo na rede aleatória, uma técnica de conectividade finita foi utilizada, na qual cada spin é conectado a um número finito de outros spins. Os spins foram conectados de acordo com uma distribuição de Poisson, os termos de campo aleatório seguiram uma distribuição bimodal e as interações entre os spins foram consideradas uniformes. Desse modo, só há desordem nas conexões entre os spins. O foco desse trabalho foi determinar como a natureza da transição de fase é alterada com a conectividade e se há um comportamento reentrante das linhas de transição de fase. A técnica de réplicas é usada para obter equações de ponto de sela para a distribuição de campos locais. Um Ansatz de simetria de réplicas foi utilizado para a função de ordem e esse foi escrito em termos de uma distribuição bidimensional de campos efetivos, onde uma das componentes é associada com um termo linear dos spins e a outra com o termo de campo cristalino. Com isso, equações para as funções de ordem e a energia livre podem ser obtidas. Uma técnica de dinâmica populacional é usada para resolver numericamente a equação auto-consistente para a distribuição de campos locais e outros parâmetros, como a magnetização, a atividade da rede e a energia livre. Os resultados indicam que a natureza da transição ferromagnética-paramagnética, a posição do ponto tricrítico e a existência de reentrância dependem fortemente do valor da conectividade e, nos casos com um termo de campo aleatório, dependem da intensidade dos campos aleatórios. No caso em que o campo cristalino é aleatório, o ponto tricrítico é suprimido para valores acima de um certo valor de aleatoriedade. / The present work studies the Blume-Capel model in a random network and also analyses the inclusion of a random crystal-field term and a random field term. To solve the model in a random network a finite connectivity technique is used, in which each spin is connected to a finite number of other spins. The spins were connected according a Poisson distribution, the random field terms followed a bimodal distribution and the bonds between the spins were considered uniform. Thus, there is only a connection disorder. The focus of this work was on determining how the nature of the phase transition changes with the connectivity and the random fields and if there is a reentrant behavior of the phase boundaries. The replica technique is used to obtain saddle-point equations for the effective local-field distribution. The replica symmetric Ansatz for the order function is written in terms of a two-dimensional effective-field distribution, where one of the components is associated with a linear form in the spins and the other with the crystal-field term. This allows one to derive equations for the order function and for the free-energy. A population dynamics procedure is used to solve numerically a self-consistency equation for the distribution of the local field and with it some physical parameters, like magnetization and free-energy. The results obtained indicate that the nature of the F-P transition, the location of the tricritical point and the presence of a reentrant phase depend strongly on the connectivity. In the cases with a random field term, those are also dependent on the intensity of the fields. For the case with a random crystal-field term, the tricritical point is supressed above a certain value of randomness.

O presente trabalho estuda o modelo de Blume-Capel na rede aleatória e também analisa a inclusão de um termo de campo cristalino aleatório e de um termo de campo local aleatório. Ao resolver o modelo na rede aleatória, uma técnica de conectividade finita foi utilizada, na qual cada spin é conectado a um número finito de outros spins. Os spins foram conectados de acordo com uma distribuição de Poisson, os termos de campo aleatório seguiram uma distribuição bimodal e as interações entre os spins foram consideradas uniformes. Desse modo, só há desordem nas conexões entre os spins. O foco desse trabalho foi determinar como a natureza da transição de fase é alterada com a conectividade e se há um comportamento reentrante das linhas de transição de fase. A técnica de réplicas é usada para obter equações de ponto de sela para a distribuição de campos locais. Um Ansatz de simetria de réplicas foi utilizado para a função de ordem e esse foi escrito em termos de uma distribuição bidimensional de campos efetivos, onde uma das componentes é associada com um termo linear dos spins e a outra com o termo de campo cristalino. Com isso, equações para as funções de ordem e a energia livre podem ser obtidas. Uma técnica de dinâmica populacional é usada para resolver numericamente a equação auto-consistente para a distribuição de campos locais e outros parâmetros, como a magnetização, a atividade da rede e a energia livre. Os resultados indicam que a natureza da transição ferromagnética-paramagnética, a posição do ponto tricrítico e a existência de reentrância dependem fortemente do valor da conectividade e, nos casos com um termo de campo aleatório, dependem da intensidade dos campos aleatórios. No caso em que o campo cristalino é aleatório, o ponto tricrítico é suprimido para valores acima de um certo valor de aleatoriedade. / The present work studies the Blume-Capel model in a random network and also analyses the inclusion of a random crystal-field term and a random field term. To solve the model in a random network a finite connectivity technique is used, in which each spin is connected to a finite number of other spins. The spins were connected according a Poisson distribution, the random field terms followed a bimodal distribution and the bonds between the spins were considered uniform. Thus, there is only a connection disorder. The focus of this work was on determining how the nature of the phase transition changes with the connectivity and the random fields and if there is a reentrant behavior of the phase boundaries. The replica technique is used to obtain saddle-point equations for the effective local-field distribution. The replica symmetric Ansatz for the order function is written in terms of a two-dimensional effective-field distribution, where one of the components is associated with a linear form in the spins and the other with the crystal-field term. This allows one to derive equations for the order function and for the free-energy. A population dynamics procedure is used to solve numerically a self-consistency equation for the distribution of the local field and with it some physical parameters, like magnetization and free-energy. The results obtained indicate that the nature of the F-P transition, the location of the tricritical point and the presence of a reentrant phase depend strongly on the connectivity. In the cases with a random field term, those are also dependent on the intensity of the fields. For the case with a random crystal-field term, the tricritical point is supressed above a certain value of randomness.

We study the metastability of magnetic nanoparticles with size distributions. We simulate an array of magnetic nanoparticles with a spin S = 1 ferromagnetic Blume-Capel model on a square lattice. Studying decays of the metastable state in the Blume-Capel model at low temperatures requires an extremely long computational time in kinetic Monte Carlo simulations. Therefore, we use an advanced algorithm adapted from the Monte Carlo with absorbing Markov chain algorithm for the Ising model in order to study the Blume-Capel model with size distributions. We modeled the particle size distributions as distributions of magnetic anisotropy. We compute the low-temperature average lifetime of the magnetization relaxation using kinetic Monte Carlo simulations with the advanced algorithms. We also calculate the lifetime using the absorbing Markov chains method for analytical results. Our results show that the lifetime of the metastable state follows a modified-Arrhenius law where the energy barrier has a dependency on temperature and standard deviation of the distributions in addition to magnetic field and magnetic anisotropy. The magnetic anisotropy barrier is determined by the smallest particle within a given distribution. We also study magnetization relaxation in different single critical droplet regions using different dynamics: Glauber and phonon-assisted dynamics. We find that the lifetime follows the modified-Arrhenius law for both dynamics, and an explicit form of the lifetime differs in different regions for different dynamics. For the Glauber dynamics, the Arrhenius prefactor does not depend on the standard deviation of the distribution of the magnetic anisotropy. For the phonon-assisted dynamics, however, even the prefactor of the lifetime depends on the standard deviation and is significantly reduced for a wide distribution of magnetic anisotropy. Furthermore, the phonon-assisted dynamics forbids transitions between degenerate energy states and results in an increase of the energy barrier at the single critical droplet region boundary compared to that for the Glauber dynamics. We find that the spin system with a distribution of magnetic anisotropy finds lower-energy relaxation pathways to avoid degenerate state, and the energy barrier becomes the same for both dynamics. / Ph. D.

This research is the outcome of investigations of the ability of Nitella congesta, a charophyte, to hyperaccumulate metal contaminants, as well as contribute to the sustainable development of a chain of lakes derived from the sand mine voids at Capel 250km south of Perth, Western Australia. Studies were conducted to ascertain the taxonomy of Nitella congesta as well as its life cycle pattern in relation to the hydrological regime of the lakes of the wetlands. It was observed that a decrease in the availability of water in the lakes particularly on the onset of summer, initiated the production of fruiting bodies whiles prolonged availability of water ensured a prolonged vegetative growth. / Aquatic plants play an important role in the structuring of freshwater communities. Freshwater macrophytes such as Nitella congesta have been reported to serve as food source as well as provide refuge and shelter for macroinvertebrates. Thus the presence of freshwater macrophytes in one way or the other has a direct impact on the species abundance and diversity of macroinvertebrates that use them as their habitat. A study of the impact of Nitella congesta as a suitable macrophyte on diversity and abundance of macroinvertebrates showed a positive outcome. It was observed that species richness and diversity were high in Nitella congesta dominated sites of the lakes. Experimental outcome showed that Nitella congesta is a hyperaccumulator of metals. Both the mucilage and the thallus displayed concentrations of few metals. / The disappearance of submerged macrophytes such as charophytes in shallow lakes is a major problem caused by eutrophication. There has been an approved proposal to discharge treated waste water with a phosphorus concentration of about 4,000μg/L into the lakes of the Capel Wetlands Centre. This necessitated a study of the impact of eutrophication on the establishment of Nitella congesta as a functional macrophyte for the enhancement of the ecological structure of the wetlands. / Results showed that though eutrophication will initially increase the primary productivity of the lakes of the wetlands, the eventual consequence will be the loss of Nitella congesta as a functional macrophyte in the wetlands. / At the last stage of the study, a consistent decrease in pH readings of the lakes and lack of successful germination of Nitella congesta as a result of prolonged drought and exposure of the lake sediment was observed. This necessitated a thorough study of the impact of climate change on the establishment of Nitella congesta in the wetlands. In conclusion, it was observed that Nitella congesta could serve as a suitable tool for the rehabilitation of the wetlands.