[en] Effects of ferroquadrupolar exchange interaction J₂ on critical behavior of a frustrated classical XY model with antiferromagnetic exchange interaction J₁ are investigated on stacked triangular lattice by means of histogram Monte Carlo simulations. We identify four long-range order phases separated by the boundaries which can be either of second or first order, depending on the kind of transition and magnitude of J₁/J₂. Characteristics of the respective phases, mechanisms of their creation, and natures of the transitions between the respective phases are elaborated on

[en] Monte Carlo simulations have been used to study critical, tricritical as well as some history-dependent properties of a diluted Ising metamagnet in an external field. Phase boundaries, including location of tricritical points, have been established in a broad concentration range. A first-order transition is estimated to survive down to at least p=0.5, i.e., even in an extreme dilution region. In the region of strong dilution additional shorter simulations on lattices of large linear size have been run in order to study irreversibilities associated with the domain state formation

[en] Critical properties of a classical plane rotator spin system with ferromagnetic and antiferroquadrupolar interactions on stacked triangular lattice are investigated by histogram Monte Carlo simulations. The competing bilinear and biquadratic interactions, J₁ and J₂, respectively, and the frustrated triangular geometry bring about rather complicated critical behavior. In the range of J₁/|J₂|<2, as temperature is lowered, the system is found to pass through four phase transitions, ending in the ground state that shows no conventional LRO. We draw phase diagram in J₁/|J₂|-k_BT_c/|J₂| space, classify the respective phase transitions and elaborate on reasons of the low-temperature disorder

[en] The three-dimensional XY model with bilinear-biquadratic exchange interactions J and J', respectively, has been studied by Monte Carlo simulations. From the detailed analysis of the thermal variation of various physical quantities, as well as the order parameter and energy histogram analysis, the phase diagram including two different ordered phases has been determined. There is a single phase boundary from a paramagnetic to a dipole-quadrupole ordered phase, which is of second order in a high J/J' ratio region, changing to a first-order one for 0.35≤J/J'≤0.5. Below J/J'=0.35 there are two separate transitions: the first one to the quadrupole long-range order (QLRO) phase at higher temperatures, followed by another one to the dipole-quadrupole long-range order (DLRO) phase at lower temperatures. The finite-size scaling analysis yields values of the critical exponents for both the DLRO and QLRO transitions close to the values for the conventional XY model which includes no biquadratic exchange

[en] Recently, a significant attention has been directed toward so called ‘acoustic metamaterials’ which have large similarity with already-known ‘electromagnetic metamaterials’ which are applied for elimination of the electromagnetic waves. The stop of electromagnetic waves is realized with the negative refractive index, negative permittivity and negative permeability. Motivated by the mathematical analogy between acoustic and electromagnetic waves, the acoustic metamaterials are introduced. It was asked the material to have negative effective mass. To obtain the negative effective mass, the artificial material, usually composite, has to be designed. The basic unit is a vibration absorber which consists of a lumped mass attached with a spring to the basic mechanical system. The purpose of the unit is to give a band gap where some frequencies of acoustic wave are stopped. We investigated the nonlinear mass-in-mass unit excited with any periodic force. Mathematical model of the motion is a system of two coupled strongly nonlinear and nonhomogeneous second-order differential equations. The solution of equations is assumed in the form of the Ateb (inverse beta) periodic function. The frequency of vibration is obtained as the function of the parameters of the excitation force. The effective mass of the system is also determined. Regions of negative effective mass are calculated. For these values the motion of the forced mass stops. It is concluded that the stop frequency gaps are much wider for the nonlinear than for the linear system. Based on the obtained parameter values, the acoustic metamaterial could be designed.

[en] In this paper, the dynamics of a nonlinear smooth and discontinuous oscillator, modeled as a string–mass structure, is analyzed. This structure is convenient to be installed in vibration damping systems of high buildings for their protection in the case of earthquakes. The considered string–mass structure contains a translator movable mass connected with two strings. The motion of the mass is oscillatory and perpendicular to the string’s position. Usually, in strings preloading forces act. Due to geometric and physical properties of the system, the restitution force of the string is nonlinear. The model of the mass motion is a strong nonlinear second-order differential equation. The nonlinearity is of power type, and the order of nonlinearity is any positive real number. An exact solution of the truly nonlinear equation is introduced in the form of the Ateb function (inverse Beta function). Based on the exact solution, the approximate solving procedure of the nonlinear equation of motion is developed. The method is suitable for dynamic analyses of the system. The influence of the preloading force on the nonlinear vibrations of the string–mass system is considered. It is concluded that variation of the string force has influence on the velocity of the amplitude decrease in the system.

[en] This study is concerned with autoparametric interaction in a four degree of freedom damped mechanical system consisting of two identical pendula fitted onto a horizontal massive rod which can oscillate vertically and rotationally. One pendulum is harmonically excited. The equations of motion indicate that autoparametric interaction is possible by means of typical external and internal resonance conditions involving the system natural frequencies and excitation frequency. An intriguing phenomenon is demonstrated when the unforced pendulum is decoupled and no energy goes into it, as a result of which it stops oscillating. Numerical simulations are carried out to determine when and why this phenomenon occurs for a different excitation magnitude as well as for zero and non-zero initial conditions of the unforced pendulum.

[en] The effects of both an exchange anisotropy and a single-ion anisotropy on the phase diagram and magnetization curves of the ferromagnetic mixed spin-3/2 and spin-1/2 Heisenberg model are investigated by the use of an Oguchi approximation. Although the theory is developed for lattices with general coordination number z, we treat in detail numerically the model on the simple cubic lattice (z=6). In particular, some outstanding features are found in the ground-state behaviours of sublattice and total magnetizations. The origin and nature of the ordered phase in the quantum mixed-spin system at the low temperature region are also discussed. - Research Highlights: →We find eigenvalues and eigenvectors of the mixed-spin anisotropic Heisenberg model. →We determine phase diagrams of the mixed-spin quantum Heisenberg and Ising models. →We find difference between the quantum and classical models at low temperatures. →Physically, we ascribe this difference to the quantum fluctuation effects.

[en] By means of standard and histogram Monte Carlo simulations, we investigate the critical and compensation behaviour of a ternary mixed spin alloy of the type AB_pC_1-p on a cubic lattice. We focus on the case with the parameters corresponding to the Prussian blue analog (Ni_p^IIMn_1-p^II)_1.5[Cr^III(CN)₆].nH₂O and confront our findings with those obtained by some approximative approaches and the experiments.

[en] Effect of biquadratic exchange on phase transitions of a planar classical Heisenberg (or XY) ferromagnet on a stacked triangular lattice is investigated by standard Monte Carlo and histogram Monte Carlo simulations in the region of a bilinear to biquadratic exchange interaction ratio J₁/J₂⩽1. The biquadratic exchange is found to cause separate second-order phase transitions in a strong biquadratic exchange limit, followed by simultaneous dipole and quadrupole ordering, which is of first order for an intermediate range of the exchange ratio and changes to a second-order one again as J₁/J₂ is further increased. Thus, a phase diagram featuring both triple and tricritical points is obtained. Furthermore, a finite-size scaling analysis is used to calculate the critical indices for both dipole and quadrupole kinds of ordering.