Boundary critical behaviour of two-dimensional random Ising models (original) (raw)
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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.
Critical behavior of the 3D Ising model on a poissonian random lattice
2008
The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D-ferromagnetic Ising model on three dimensional Voronoi-Delaunay lattices. It is assumed that the coupling factor J varies with the distance r between the first neighbors as J(r) ∝ e −ar , with a ≥ 0. The critical exponents γ/ν, β/ν , and ν are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure three-dimensional ferromegnetic Ising model.
Self-averaging in the random two-dimensional Ising ferromagnet
Physical Review E
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 ln ln(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.
From surface to random criticality in layered planar Ising models
1994
A general case of a spatially nonuniform planar layered Ising model, or an equivalent quantum Ising chain, is analysed with an exact functional real space renormalization group. Various surface, finite size, quasiperiodic and random layer (McCoy-Wu) universality classes are obtained and discussed within a single theoretical framework leading to new insights into the nature of random criticality.
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...