Monte Carlo Simulations of a Disordered Binary Ising Model (original) (raw)
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Revista Mexicana de Fisica
We used a Monte Carlo simulation to analize the magnetic behavior of Ising model of mixed spins S A i = ±3/2, ±1/2 and σ B j = ±5/2, ±3/2, ±1/2, on a square lattice. Were studied the possible critical phenomena that may emerge in the region around the multiphase point (D/|J1| = −3, J2/|J1| = 1) and the dependence of the phase diagrams with the intensities of the anisotropy field of single ion (D/|J 1 |) and the ferromagnetic coupling of exchange spin S A i (J 2 /|J 1 |). The system displays first order phase transitions in a certain range of the parameters of the Hamiltonian, which depend on D/|J 1 | and |J 2 /|J 1 |. In the plane (D/|J 1 |, k B T /|J 1 |), the decrease of |D/|J 1 ||, implies that the critical temperature, T c , increases and the first order transition temperature, T t , decreases. In the plane (J2/|J1|, kBT /|J1|), Tc increases with the increasing of J2/|J1|, while that Tt decreases.
2020
In this paper, we theoretically study the critical properties of the classical spin-1 Ising model using two approaches: 1) the analytical low-temperature series expansion and 2) the numerical Metropolis Monte Carlo technique. Within this analysis, we discuss the critical behavior of one-, two- and three-dimensional systems modeled by the first-neighbor spin-1 Ising model for different types of exchange interactions. The comparison of the results obtained according the Metropolis Monte Carlo simulations allows us to highlight the limits of the widely used mean-field theory approach. We also show, via a simple transformation, that for the special case where the bilinear and bicubic terms are set equal to zero in the Hamiltonian the partition function of the spin-1 Ising model can be reduced to that of the spin-1/2 Ising model with temperature dependent external field and temperature independent exchange interaction times an exponential factor depending on the other terms of the Hamilt...
Physical Review E, 1999
The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to put the equilibrium ensemble approach to work. A new method to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open in both directions. A critical discussion shows that, still, an unambiguous discrimination between the two scenarios is not possible on the basis of the available finite size data.
Critical Behavior of the Quenched Random Mixed-Spin Ising Model
International Journal of Modern Physics C
In this work, we simulated a quenched random mixed-spin Ising model on the square lattice. The model system consists of two different particles with spins σ = 1/2 (states ±1/2) and S = 1 (states ±1, 0). These particles are randomly distributed on the lattice, and we considered only nearest-neighbor interactions. This model can represent a random magnetic binary alloy AxB1-x, obtained from the high-temperature quenching of a liquid mixture. We performed Monte Carlo simulations for several lattice sizes and temperatures, and we found its critical temperature through the reduced fourth-order cumulant. We also determined the magnetization, the susceptibility, and the specific heat as a function of temperature. We used finite-size scaling arguments to estimate the critical exponents β, γ, and ν of the model. We showed that the quenched model is in the same universality class of the two-dimensional pure Ising model. We also investigated the sample to sample fluctuations that occur in the ...
2021
We studied the critical behavior of the J1 − J2 spin-1/2 Ising model in the square lattice by considering J1 fixed and J2 as random interactions following discrete and continuous probability distribution functions. The configuration of J2 in the lattice evolves in time through a competing kinetics using Monte Carlo simulations leading to a steady state without reaching the free-energy minimization. However, the resulting non-equilibrium phase diagrams are, in general, qualitatively similar to those obtained with quenched randomness at equilibrium in past works. Accordingly, through this dynamics the essential critical behavior at finite temperatures can be grasped for this model. The advantage is that simulations spend less computational resources, since the system does not need to be replicated or equilibrated with Parallel Tempering. A special attention was given for the value of the amplitude of the correlation length at the critical point of the superantiferromagnetic-paramagnet...
Critical and thermodynamic properties of the randomly dilute Ising model
Physical Review B, 1978
The randomly bond-dilute two-dimensional nearest-neighbor Ising model on the square lattice is studied by renormalization-group methods based on the Migdal-Kadanoff approximate recursion relations. Calculations give both thermal and magnetic exponents associated with the percolative fixed point. DifFerential recursion relations yield a phase diagram which is in quantitative agreement with all known results. Curves for the specific heat, percolation probability, and magnetization are displayed. The critical region of the specific heat becomes unobservably narrow well above the percolation threshold p, , This provides a possible explanation for the apparent specific-heat rounding in certain experiments.
Monte Carlo study of growth in the two-dimensional spin-exchange kinetic Ising model
Physical Review B, 1988
Results obtained from extensive Monte Carlo simulations of domain growth in the twodimensional spin-exchange kinetic Ising model with equal numbers of up and down spins are presented. Using difterent measures of domain sizeincluding the pair-correlation function, the energy, and circularly-averaged structure factorthe domain size is determined (at T =0.5T,) as a function of time for times up to 10 Monte Carlo steps. The growth law R(t)= A +Bt'/ is found to provide an excellent fit (within 0.3%) to the data, thus indicating that at long times the classical value of-, for the exponent is correct. It is pointed out that this growth law is equivalent to an effective exponent for a1I times (as given by Huse) n, z(t)=-, '-, 'C/8 (t). No evidence for logarithmic behavior is seen. The self-averaging properties of the various measures of domain size and the variation of the constants A and 8 with temperature are also discussed. In addition, the scaling of the structure factor and anisotropy efrects due to the lattice are examined.
Temperature-dependent criticality in random 2D Ising models
The European Physical Journal Plus, 2021
We consider 2D random Ising ferromagnetic models, where quenched disorder is represented either by random local magnetic fields (random-field Ising model) or by a random distribution of interaction couplings (random-bond Ising model). In both cases, we first perform zero- and finite-temperature Monte Carlo simulations to determine how the critical temperature depends on the disorder parameter. We then focus on the reversal transition triggered by an external field and study the associated Barkhausen noise. Our main result is that the critical exponents characterizing the power law associated with the Barkhausen noise exhibit a temperature dependence in line with existing experimental observations.