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Scientia Plena

Estudo do Comportamento Crítico do Modelo Ising com Interações Mistas Através de Técnicas Analíticas e Computacionais

J.B. Santos-Filho, N. O. Moreno, Douglas F. de Albuquerque

Published Jan 1, 2007• 0 citations
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Abstract

The critical properties of a random mixed-bond Ising model on a cubic lattice are studied so much  numerically with analytically. Analytical studies on Mixed-bond Ising model through renormalization  group technique predict the existence of reentrant magnetism in certain range of values of the  competition parameter α. This phenomenon typically found in systems that present spin-glass phase. In  this work, did we use the algorithm cluster of Wolff to simulate the dynamics of the system. Using the  technique of the Histogram obtains the thermodynamic amounts of interest and based on the theory finite  size scaling found the critical temperatures, the phase diagrams and the critical exponents of the model. Our results were compared with those obtained using a new technique in effective field theory which  employs similar probability distribution within the framework of two-site clusters.

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•Nov 26, 2013•0 citations
The critical properties of a random mixed-bond Ising model on a cubic lattice are studied so much  numerically with analytically. Analytical studies on Mixed-bond Ising model through renormalization  group technique predict the existence of reentrant magnetism in certain range of values of the  competition parameter α. This phenomenon typically found in systems that present spin-glass phase. In  this work, did we use the algorithm cluster of Wolff to simulate the dynamics of the system. Using the  technique of the Histogram obtains the thermodynamic amounts of interest and based on the theory finite  size scaling found the critical temperatures, the phase diagrams and the critical exponents of the model. Our results were compared with those obtained using a new technique in effective field theory which  employs similar probability distribution within the framework of two-site clusters.
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied bothnumerically and analytically. Analytical studies on Mixed-bond Ising model by using renormalizationgroup technique predict the existence of reentrant magnetism in a certain range of values of thecompetition parameter α. This phenomenon typically is found in systems presenting spin glass phase, forinstance EupSr1-p. We seek the existence of the reentrance by means of Monte Carlo simulations. In thiswork, we use the Cluster algorithms de Wolff to simulate the dynamics of the system. We obtained thethermodynamic quantities such as magnetization and susceptibility. Critical temperatures were estimatedof the maximum of the susceptibility and with these values we made the phase diagram Tc versus p fordifferent α values. Our results were compared with those obtained using a new technique in effective fieldtheory which employs similar probability distribution within the framework of two-site clusters.
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Metropolis and Wolff algorithm with histogram technique and finite size scaling theory to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters.
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Cluster algorithms of Wolff and Glauber to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters
A transicao de fase do modelo de Ising com ligacoes mistas (Mixed-bond) numa rede cubica e estudada tanto numericamente com analiticamente. Analiticamente estudos do modelo de Ising mixed-bond atraves de tecnica de grupo de renormalizacao predizem a existencia de reentrâncias magneticas em certos valores do parâmetro de competicao α (α positivo). Este fenomeno e tipicamente encontrado em sistemas (a exemplo do composto EupSr1-p) que apresentam fase vidro-de-spin (spin-glass). Neste trabalho, usamos o algoritmo cluster de Wolff para simular a dinâmica do sistema e obter as quantidades termodinâmicas magnetizacao e susceptibilidade magnetica. A temperatura critica do sistema foi estimada do maximo de susceptibilidade e com estes valores construimos o diagrama de fase Tc versus p para diferentes valores de α ( 0 > α ). Nossos resultados foram comparados como aqueles obtidos pelo metodo de teoria de campo efetivo que emprega uma distribuicao de probabilidade similar dentro de uma estrutura de cluster com dois spins.
In this work we study the magnetic properties of the ferromagnetic Ising model on a square lattice, in zero external magnetic eld, through Monte Carlo simulations. The initial part comprises the theoretical background and the simulations as the Monte Carlo code, the single histogram technique and the estimate of the error bars. For the particular four-spin cluster the exact results have been obtained and compared to the simulational ones. Such comparison granted a better understanding of the process of generating the computational data besides a way of conrming the correctness of the code. Together with the single histogram technique and the nite size scaling hypothesis. We have obtained the mean values of the magnetization, energy, specic heat, susceptibility and the Binder cumulant. It was possible to obtain the thermodynamic quantities as a function of temperature and the system size. It was evident the existence of a phase transition with its peculiar behavior. Accordingly, we have obtained the critical temperature as well as the critical exponents of the model. The values of the critical indices and the critical temperature agree well with the exact ones and those coming from other computational methods.
The thermodynamic properties of spin models on the lattice have been studied by employing phenomenological renormalization group techniques. The spin-1 Blume- Capel model and the spin-1 and spin-3/2 Baxter-Wu model have been treated. The Blume Capel model with spin-1, in its diluted version, on the simple cubic lattice has been studied by using the mean field renormalization group in the pair aproximation. We have obtained the critical temperature as a function of the vacant sites concentration as well a function of the crystal field anisotropy. We consider exchange e superexchange interactions between Fe atoms induzed by Al atoms and applied this model to FeAl alloys to describe its thermodynamics properties. We also studied the spin-1 and 3/2 Baxter-Wu model in a crystal field by employing the finite size renormalization group approach. The eigenvalues of the transfer matrix have been computed in order to get the corresponding phase diagram. Estimates of the firstand second-order transition temperatures have been obtained, as well as multicritical points, critical exponents and central charges, the latter two being obtained for some values of the crystal field. The Gibbs phase rule has been used to check the consistency of the phase diagram of some magnetic models, including those treated in this work. In this case it is necessary to take into account the symmetries carried by the magnetic Hamiltonians.