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arXiv:1002.0100

Phase Diagram of mixed bond Ising systems by use of Monte Carlo and the effective-field theory

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

Published Jan 31, 2010• 0 citations
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Abstract

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

DOI
10.48550/arxiv.1002.0100

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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
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 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 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 dynamical phase transitions of the kinetic Ising model in the presence of a random magnetic field with a bimodal probability distribution is studied by using effective-field theory (EFT) with correlations. We have used a Glauber-type stochastic dynamic to describe the time evolution of the system, where the system strongly depends on the H≡√<H(i)(2)>(c) root mean square deviation of the magnetic field. The EFT dynamic equation is given for the simple cubic lattice (z=6), and the dynamic order parameter is calculated. The system presents ferromagnetic and paramagnetic states for low and high temperatures, respectively. Our results predict first-order transitions at low temperatures and large disorder strengths, which corresponds to the existence of a nonequilibrium tricritical point (TCP) in a phase diagram in the T-H plane. We compare the results with the equilibrium phase diagram, where only the first-order line is different. Our qualitative results are compatible with recent Monte Carlo simulations.
We apply numerical simulations to study the criticality of the 3D Ising model with random site quenched dilution. The emphasis is given to the issues not being discussed in detail before. In particular, we attempt a comparison of different Monte Carlo techniques, discussing regions of their applicability and advantages/disadvantages depending on the aim of a particular simulation set. Moreover, besides evaluation of the critical indices we estimate the universal ratio Γ+/Γ−Γ^+/Γ^-Γ+/Γ− for the magnetic susceptibility critical amplitudes. Our estimate Γ+/Γ−=1.67±0.15Γ^+/Γ^- = 1.67 \pm 0.15Γ+/Γ−=1.67±0.15 is in a good agreement with the recent MC analysis of the random-bond Ising model giving further support that both random-site and random-bond dilutions lead to the same universality class.
We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to $128000\ensuremath{\approx}{50}^{3}$ sites which are linked together according to the Voronoi-Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and ${\ensuremath{\varphi}}^{4}$ field theory on three-dimensional regular cubic lattices.