Effective-field-theory analysis of the three-dimensional random-field Ising model on isometric lattices (original) (raw)

The 3d random field Ising model at zero temperature

Europhysics Letters (EPL), 1997

We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes L in three dimensions. For each random field configuration we vary the ferromagnetic coupling strength J. We find that in the infinite volume limit the magnetization is discontinuous in J. The energy and its first J derivative are continuous. The approch to the thermodynamic limit is slow, behaving like L −p with p ∼ .8 for the gaussian distribution of the random field. We also study the bimodal distribution hi = ±h, and we find similar results for the magnetization but with a different value of the exponent p ∼ .6. This raises the question of the validity of universality for the random field problem.

Ground-state numerical study of the three-dimensional random-field Ising model

Physical Review B, 2003

The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 60^3. For each realization of the normalized random fields, the strength of the random field, Delta and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the H-Delta plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.

The Ising antiferromagnet on an anisotropic simple cubic lattice in the presence of a magnetic field

arXiv: Statistical Mechanics, 2012

We have studied the anisotropic three-dimensional nearest-neighbor Ising model with competitive interactions in an uniform longitudinal magnetic field HHH. The model consists of ferromagnetic interaction Jx(Jz)J_{x}(J_{z})Jx(Jz) in the x(z)x(z)x(z) direction and antiferromagnetic interaction JyJ_{y}Jy in the yyy direction. We have compared our calculations within a effective-field theory in clusters with four spins (EFT-4) in the simple cubic (sc) lattice with traditional Monte Carlo (MC) simulations. The phase diagrams in the h−kBT/Jxh-k_{B}T/J_{x}h−kBT/Jx plane ($h=H/J_{x}$) were obtained for the particular case lambda1=Jy/Jx(lambda2=Jz/Jx)=1\lambda_{1}=J_{y}/J_{x} (\lambda_{2}=J_{z}/J_{x})=1lambda1=Jy/Jx(lambda2=Jz/Jx)=1 (anisotropic sc). Our results indicate second-order frontiers for all values of HHH for the particular case lambda2=0\lambda_{2}=0lambda2=0 (square lattice), while in case lambda1=lambda2=1\lambda_{1}=\lambda_{2}=1lambda1=lambda2=1, we observe first- and second-order phase transitions in the low and high temperature limits, respectively, with presence of a tricritical point. Using EFT-4, a reentran...

3-DIMENSIONAL Ferromagnetic Ising-Models with Quenched, Random Nonmagnetic Impurities

Physica B & C, 1986

We investigate the thermal and magnetic properties of three-dimensional, ferromagnetic Ising models with quenched and random non-magnetic (site) impurities in the case of simple cubic lattices. The reported thermodynamic phase diagrams reveal in particular a sharp phase transition (e.g. in the magnetic susceptibility) for the (relatively small) impurity concentrations

Monte-Carlo simulation of phase transition in 2D and 3D ising model

Scientific World

In this work, Markov Chain-Monte Carlo technique was used to study the phase transition in two and three dimensional Ising Model (IM) in a square and cubic lattice. The study of temperature dependence of average magnetization and specific heat in different magnetic fields has been carried out in the 3x3 and 3x3x3 lattice with periodic boundary. Critical temperature point kBTc / J for 2D and 3D Ising Model has been observed at around 2.2 and 4.3 respectively at zero field. Our work satisfies Onsager’s critical value in 2D IM. The simulation suggests bifurcation in average magnetization below critical temperature Tc. Temperature plays the role of increasing randomness of spins. We found that Ising Model in small lattice size still retains interesting features like spontaneous magnetization and symmetry breaking below Tc at B = 0. At a non-zero field, the likelihood of spins to prefer certain alignment depends on the direction of the external field and magnitude of magnetization depend...

Mean field study of the mixed Ising model in a random crystal field

Physica A-statistical Mechanics and Its Applications, 2008

The magnetic properties of a mixed Ising ferrimagnetic system, in which the two interacting sublattices have spins σ, (±1/2) and spins S, (±1,0) in the presence of a random crystal field, have been studied with the mean field approach. The obtained results show the existence of some interesting phenomena, such as the appearance of a new ferrimagnetic phase, namely, partly ferrimagnetic phase (mσ=12,mS=−12) and consequently the existence of four topologically different types of phase diagrams. Furthermore, compensation behaviour and re-entrant phenomenon are found for appropriate ranges of crystal field. Thermal magnetization behaviour and phase diagrams have been discussed in detail.

Effect of a random longitudinal field and crystal field on a decorated ferrimagnetic Ising model

Journal of Magnetism and Magnetic Materials, 2007

The phase diagrams and magnetic properties of a decorated two-sublattices ferrimagnetic Ising models consisting of two magnetic atoms A and B with S A S A ¼ 1 2 À Á and S B S B 4 1 2 À Á are investigated by the use of an effective field theory based on a probability distribution method. The effects of the uniaxial crystal field D (on the B atoms) and the random longitudinal field, on the behavior of the system, are examined. We find a number of characteristic phenomena, such as the possibility of two compensation points, the re-entrant behavior and the existence of tricritical points.

Nonequilibrium athermal random-field Ising model on hexagonal lattices

Physical review, 2021

We present the results of a study providing numerical evidence for the absence of critical behavior of the nonequilibrium athermal random-field Ising model in adiabatic regime on the hexagonal two-dimensional lattice. The results are obtained on the systems containing up to 32 768 × 32 768 spins and are the averages of up to 1700 runs with different random-field configurations per each value of disorder. We analyzed regular systems as well as the systems with different preset conditions to capture behavior in thermodynamic limit. The superficial insight to the avalanche propagation in this type of lattice is given as a stimulus for further research on the topic of avalanche evolution. With obtained data we may conclude that there is no critical behavior of random-field Ising model on hexagonal lattice which is a result that differs from the ones found for the square and for the triangular lattices supporting the recent conjecture that the number of nearest neighbors affects the model criticality.

The magnetization of the 3D Ising model

Journal of Physics A: Mathematical and General, 1996

We present highly accurate Monte Carlo results for simple cubic Ising lattices containing up to 256 3 spins. These results were obtained by means of the Cluster Processor, a newly built special-purpose computer for the Wolff cluster simulation of the 3D Ising model. We find that the magnetization M(t) is perfectly described by M(t) = (a 0 − a 1 t θ − a 2 t)t β , where t = (T c − T )/T c , in a wide temperature range 0.0005 < t < 0.26. If there exist corrections to scaling with higher powers of t, they are very small. The magnetization exponent is determined as β = 0.3269 (6). An analysis of the magnetization distribution near criticality yields a new determination of the critical point: K c = J/k B T c = 0.2216544, with a standard deviation of 3·10 −7 .

Two-dimensional Ising model with annealed random fields

Physica A: Statistical Mechanics and its Applications, 1988

We investigate the influence of annealed random fields on the phase diagram of the ferromagnetic Ising model on the square lattice. We find that the gaussian random field makes the ferromagnetic ground state unstable and we have a super-antiferromagnetic state at low temperatures. For the binary random field, in which the random field takes +h with probability p and-h with probability 1-p, there is a critical field h,, and the ferromagnetic ground state is stable for h < h, but unstable for h > h,. When the ferromagnetic ground state is unstable, we have a re-entrant phase transition. * Work partially financed by the Brazilian Agencies CNPq and Finep.