Boundary critical behaviour of two-dimensional random Ising models (original) (raw)
Surface Critical Behavior of Two-Dimensional Dilute Ising Models
Journal of Statistical Physics, 1997
Ising models with nearest neighbor ferromagnetic random couplings on a square lattice with a (1, 1) surface are studied, using Monte Carlo techniques and a star-triangle transformation method. In particular, the critical exponent of the surface magnetization is found to be close to that of the perfect model, Β1 = 1/2. The crossover from surface to bulk critical properties is discussed.
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.
Physical review, 2019
In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder R c (l) and the critical magnetic field H c (l) under different boundary conditions when the system thickness l varies. We propose expressions for R c (l) and H c (l) as well as for the effective critical disorder R eff c (l, L) and effective critical magnetic field H eff c (l, L) playing the role of the effective critical parameters for the L × L × l lattices of finite lateral size L. We support these expressions by the scaling collapses of the magnetization and susceptibility curves obtained in extensive simulations. The collapses are achieved with the two-dimensional (2D) exponents for l below some characteristic value, providing thus a numerical evidence that the thin systems exhibit a 2D-like criticality which should be relevant for the experimental analyses of thin ferromagnetic samples.
Monte Carlo study of the surface critical phenomena of the Ising model
1985
Monte Carlo technique is applied to the three•dimensional Ising model with free surface. The critical behavior of the layer magnetization, the layer susceptibility and the local susceptibility near the ordinary transition point is investigated. The universal properties of the surface critical exponents and the surface critical amplitude ratios are confirmed. The scaling of magnetization profile is studied, and the bulk amplitude ratio for the correlation length ~o h / ~o-is calculated.
Self-averaging in the random 2D Ising ferromagnet
2017
We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size L like ∼ L (L). In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a δ-peak in the thermodynamic limit L →∞. While previously a lack of self-averaging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.
Physical Review Letters, 2000
The critical behaviour of the randomly spin-diluted Ising model in two space dimensions is investigated by a new method which combines a grand ensemble approach to disordered systems proposed by Morita with the phenomenological renormalization group scheme of Nightingale. Accurate approximations for the phase diagram and for the connectivity length exponent of the percolation transition are obtained. Our results suggest that the thermal phase transition of the disordered system might be different from that of the pure system: we observe a continuous variation of critical exponents with the density ρ of magnetic impurities, respecting, however, weak universality in the sense that η and γ/ν do not depend on ρ while γ and ν separately do. Our results are in qualitative and quantitative agreement with a recent Monte-Carlo study. * Supported by a Heisenberg fellowship
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.
Two-dimensional Dilute Ising Models: Defect Lines and the Universality of the Critical Exponent \nu
1999
We consider two-dimensional Ising models with randomly distributed ferromagnetic bonds and study the local critical behavior at defect lines by extensive Monte Carlo simulations. Both for ladder and chain type defects, non-universal critical behavior is observed: the critical exponent of the defect magnetization is found to be a continuous function of the strength of the defect coupling. Analyzing corresponding stability conditions, we obtain new evidence that the critical exponent nu\nunu of the bulk correlation length of the random Ising model does not depend on dilution, i.e. nu=1\nu=1nu=1.
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 amplitude ratio of the susceptibility in the random-site two-dimensional Ising model
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
We present a different way of probing the universality class of the site-diluted two-dimensional Ising model. We analyze Monte Carlo data for the magnetic susceptibility, introducing a fitting procedure in the critical region applicable even for a single sample with quenched disorder. This gives us the possibility to fit simultaneously the critical exponent, the critical amplitude, and the sample-dependent pseudocritical temperature. The critical amplitude ratio of the magnetic susceptibility is seen to be independent of the concentration q of the empty sites for all investigated values of q < or =0.25. At the same time the average effective exponent gamma(eff) is found to vary with the concentration q, which may be argued to be due to logarithmic corrections to the power law of the pure system. These corrections are canceled in the susceptibility amplitude ratio as predicted by theory. The central charge of the corresponding field theory was computed and compared well with the t...