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First-order phase transition in a 2D random-field Ising model with conflicting dynamics

Nuno Crokidakis

Published Nov 20, 2012• 10 citations
OpenAlex

Abstract

The effects of locally random magnetic fields are considered in a nonequilibrium Ising model defined on a square lattice with nearest-neighbors interactions. In order to generate the random magnetic fields, we have considered random variables {h} that change randomly with time according to a double-gaussian probability distribution, which consists of two single gaussian distributions, centered at +ho and −ho, with the same width σ. This distribution is very general, and can recover in appropriate limits the bimodal distribution (σ → 0) and the single gaussian one (ho = 0). We performed Monte Carlo simulations in lattices with linear sizes in the range L = 32 − 512. The system exhibits ferromagnetic and paramagnetic steady states. Our results suggest the occurence of first-order phase transitions between the above-mentioned phases at low temperatures and large random-field intensities ho, for some small values of the width σ. By means of finite size scaling, we estimate the critical exponents in the low-field region, where we have continuous phase transitions. In addition, we show a sketch of the phase diagram of the model for some values of σ. PACS numbers: 05.10.Ln, 05.50.+q, 64.60.De, 75.10Hk, 75.40.MgFirst-order phase transition in a 2D random-field Ising model with conflicting dynamics2 1.

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First-order phase transition in a 2D random-field Ising model with conflicting dynamics

Nuno Crokidakis

The effects of locally random magnetic fields are considered in a nonequilibrium Ising model defined on a square lattice with nearest-neighbor interactions. In order to generate the random magnetic fields, we have considered random variables { h } that change randomly with time according to a double-Gaussian probability distribution, which consists of two single-Gaussian distributions, centered at + h o and − h o , with the same width σ. This distribution is very general and can recover in appropriate limits the bimodal distribution ( ) and the single-Gaussian one ( h o = 0). We performed Monte Carlo simulations in lattices with linear sizes in the range L = 32–512. The system exhibits ferromagnetic and paramagnetic steady states. Our results suggest the occurrence of first-order phase transitions between the above-mentioned phases at low temperatures and large random-field intensities h o for some small values of the width σ. By means of finite size scaling, we estimate the critical exponents in the low-field region, where we have continuous phase transitions. In addition, we show a sketch of the phase diagram of the model for some values of σ.

arXiv:0901.2659•Journal of Statistical Mechanics Theory and Experiment•Feb 24, 2009•7 citations

Phase transitions in a three-dimensional kinetic spin-1/2 Ising model with random field: Effective-field-theory study

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Critical behavior of a 3-D Ising model in a random field

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CRITICAL BEHAVIOR OF THE QUENCHED RANDOM MIXED-SPIN ISING MODEL

Maurício Godoy, W. Figueiredo

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 values of the thermodynamic quantities in order to describe the self-averaging properties at the critical point.

International Journal of Modern Physics C•Jan 1, 2009•9 citations
The effects of locally random magnetic fields are considered in a nonequilibrium Ising model defined on a square lattice with nearest-neighbors interactions. In order to generate the random magnetic fields, we have considered random variables {h} that change randomly with time according to a double-gaussian probability distribution, which consists of two single gaussian distributions, centered at +ho and −ho, with the same width σ. This distribution is very general, and can recover in appropriate limits the bimodal distribution (σ → 0) and the single gaussian one (ho = 0). We performed Monte Carlo simulations in lattices with linear sizes in the range L = 32 − 512. The system exhibits ferromagnetic and paramagnetic steady states. Our results suggest the occurence of first-order phase transitions between the above-mentioned phases at low temperatures and large random-field intensities ho, for some small values of the width σ. By means of finite size scaling, we estimate the critical exponents in the low-field region, where we have continuous phase transitions. In addition, we show a sketch of the phase diagram of the model for some values of σ. PACS numbers: 05.10.Ln, 05.50.+q, 64.60.De, 75.10Hk, 75.40.MgFirst-order phase transition in a 2D random-field Ising model with conflicting dynamics2 1.
The effects of locally random magnetic fields are considered in a nonequilibrium Ising model defined on a square lattice with nearest-neighbor interactions. In order to generate the random magnetic fields, we have considered random variables { h } that change randomly with time according to a double-Gaussian probability distribution, which consists of two single-Gaussian distributions, centered at + h o and − h o , with the same width σ. This distribution is very general and can recover in appropriate limits the bimodal distribution ( ) and the single-Gaussian one ( h o = 0). We performed Monte Carlo simulations in lattices with linear sizes in the range L = 32–512. The system exhibits ferromagnetic and paramagnetic steady states. Our results suggest the occurrence of first-order phase transitions between the above-mentioned phases at low temperatures and large random-field intensities h o for some small values of the width σ. By means of finite size scaling, we estimate the critical exponents in the low-field region, where we have continuous phase transitions. In addition, we show a sketch of the phase diagram of the model for some values of σ.
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.
A Monte Carlo method has been used to study a simple cubic Ising ferromagnet in a random quenched magnetic field. The Hamiltonian for this model is ℋ==JΣ(ij)σiσj−ΣiHiσi, where σi,σj=±1, J is the nearest-neighbor interaction constant, and the field Hi=tH is fixed at each site with ti=±1 at random and Σti=0. L×L×L lattices with periodic boundary conditions have been studied for a range of H and T. As expected we find a ferromagnetic ordered state which for small H undergoes a second order phase change to the paramagnetic state with increasing temperature. A finite size scaling analysis of the preliminary data suggests that the critical exponent β is substantially smaller (β∼0.2) than the usual 3-dim Ising value of 0.31. Results obtained for small lattices indicate that below kT/J-2 the transition becomes first order suggesting that a tricritical point appears on the critcal field curve.
The nature of the three-dimensional random-field Ising model with a bimodal probability distribution is investigated using finite-time scaling combined with the Monte Carlo renormalization group method, in the presence of a linearly varying temperature. Our results support the existence of a first-order phase transition for this model, obtained through reducing the influence of finite-size effects. The critical exponents are estimated to be ν = 0.74(3), β = 0.27(1), α = − 0.023(5), and γ = 1.48(3) with corrections to the scaling. The Rushbrooke scaling law is satisfied with these exponents, and in turn identifies the asymptotic critical behavior.
We explore the critical properties of the recently discovered finite-time dynamical phase transition in the nonequilibrium relaxation of Ising magnets after a temperature quench. The transition is characterized by a sudden switch in the relaxation dynamics and it occurs at a sharp critical time. While previous works have focused either on mean-field interactions or on investigating the critical time, we analyze the critical fluctuations at the phase transition in the nearest-neighbor Ising model on a square lattice using Monte Carlo simulations. By means of a finite-size scaling analysis, we extract the critical exponents for the transition. In two spatial dimensions, we find that the exponents are consistent with those of the two-dimensional Ising universality class when the system is initially in the vicinity of the critical point. For initial temperatures below the critical one, however, the critical exponents differ from the Ising-exponents, indicating a distinct dynamical critical phenomenon.
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 values of the thermodynamic quantities in order to describe the self-averaging properties at the critical point.