In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder $R_c\left(l\right)$ and the critical magnetic field $H_c\left(l\right)$ under different boundary conditions when the system thickness $l$ varies. We propose expressions for $R_c\left(l\right)$ and $H_c\left(l\right)$ as well as for the effective critical disorder $R_c^{\mathrm{eff}}(l,L)$ and effective critical magnetic field $H_c^{\mathrm{eff}}(l,L)$ playing the role of the effective critical parameters for the $L\times L\times l$ 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.

We present numerical findings on the behavior of the athermal nonequilibrium random-field Ising model of spins at the thin striplike $L_1\times L_2\times L_3$ cubic lattices with $L_1<L_2<L_3$. Changing of system sizes highly influences the evolution and shape of avalanches. The smallest avalanches [classified as three-dimension- (3D) like] are unaffected by the system boundaries, the larger are sandwiched between the top and bottom system faces so are 2D-like, while the largest are extended over the system lateral cross section and propagate along the length $L_3$ like in 1D systems. Such a structure of avalanches causes double power-law distributions of their size, duration, and energy with larger effective critical exponent corresponding to 3D-like and smaller to 2D-like avalanches. The distributions scale with thickness $L_1$ and are collapsible following the proposed scaling predictions which, together with the distributions' shape, might be important for analysis of the Barkhausen noise experimental data for striplike samples. Finally, the impact of system size on external field that triggers the largest avalanche for a given disorder is presented and discussed.

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 $32768\times 32768$ 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.

We present a numerical study on necessary conditions for the appearance of infinite avalanche below the critical point in disordered systems that evolve throughout metastable states. The representative of those systems is the nonequilibrium athermal random-field Ising model. We investigate the impact on propagation of infinite avalanche of both the interface of flipped spins at the avalanche's starting point and the number of independent islands of flipped spins in the system at the moment when the avalanche starts. To deduce what effects are originated due to finite system's size, and to distinguish them from the real necessary conditions for the appearance of the infinite avalanche, we examined lattices of different sizes as well as other key parameters for the avalanche propagation.