2D Ising Model with Layers of Quenched Spins

The model considered is a d=2 disordered Ising system on a square lattice with nearest neighbor interaction. The disorder is induced by layers (rows) of spins, randomly located, which are frozen in an antiferromagnetic order. It is assumed that all the vertical couplings take the same positive value J _v, while all the horizontal couplings take the same positive value J _h. The model can be exactly solved and the free energy is given as a simple explicit expression. The zero-temperature entropy can be positive because of the frustration due to the competition between antiferromagnetic alignment induced by the quenched layers and ferromagnetic alignment due to the positive couplings. No phase transition is found at finite temperature if the layers of frozen spins are independently distributed, while for correlated disorder one finds a low-temperature phase with some glassy properties.     

Fixed point behavior of cumulants in the three-dimensional Ising universality class

High-order cumulants and factorial cumulants of conserved charges are suggested for the study of the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the three-dimensional Ising model which is believed to belong to the same universality class as quantum chromo-dynamics, the temperature dependence of the second- to fourth-order (factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated using the Monte Carlo method, this fixed point behavior still exists at temperatures near the critical. This fixed point behavior has also appeared in the temperature dependence of normalized factorial cumulants from at least the fourth order. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants (or fourth-order factorial cumulants) along different freeze-out curves.     

Dynamic magnetic properties of the kinetic cylindrical Ising nanotube

The nature (time variation) of response magnetizations m(wt) of the kinetic cylindrical Ising nanotube in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We have determined the time variations of m(wt) and h(wt) for various temperatures, and investigated the dynamic magnetic hysteresis behavior. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as to obtain the dynamic phase transition temperatures. We also present the dynamic phase diagrams in the three different planes and compare the results of the equilibrium and nonequilibrium states. The phase diagrams exhibit dynamic tricritical, isolated critical, multicritical and triple points. The results are in good agreement with some experimental and theoretical results.     

Spin coupling and magnetic field effects on the finite-size free energy and its non-extensivity for 1-D Ising model with nearest and next-nearest neighbor interactions in nanosystem

The effects of second-neighbor spin coupling interactions and a magnetic field are investigated on the free energies of a finite-size 1-D Ising model. For both ferromagnetic of nearest neighbor (NN) and next-nearest neighbor (NNN) spin coupling interactions, the finite-size free energy first increases and then approaches a constant value for any size of the spin chain. In contrast, when NNN and NN spin coupling interactions are antiferromagnetic and ferromagnetic, respectively, the finite-size free energy gradually decreases by increasing the competition factor and eventually vanishes for large values of it. When a magnetic field is applied, the finite-size free energy decreases with respect to the case of zero magnetic fields for both ferromagnetic and antiferromagnetic spin coupling interactions. Deviation of free energy per size for finite-size systems relative to the infinite system increases when the spin coupling interactions as well as the f parameter (the ratio of the magnetic field to NN spin coupling interaction) increase.     

Heterogeneous nucleation and depletion effect in nanowire growth

Recent experiments by Ross and co-workers proved the possibility of a mononuclear regime with heterogeneous nucleation as well as jerky growth in the vapor–liquid–solid (VLS) process for silicon nanowires. In this work, a theoretical model is presented which incorporates the effects of (i) a mononuclear regime with layer by layer growth, (i) heterogeneous nucleation of each new layer at the edge of a Au–Si droplet, (iii) drop of supersaturation after each successful nucleation and respective fast layer growth, (iv) time-dependent nucleation barrier during each new waiting period and (v) correlation between subsequent waiting periods (non-Markovian sequence of waiting periods).     

Surface/interface effects on the formation of misfit dislocation in a core–shell nanowire

The misfit strain within the core of a two-phase free-standing core–shell nanowire resulting in the generation of an edge misfit dislocation or an edge misfit dislocation dipole at the core–shell interface is considered theoretically within both the classical and surface/interface elasticity approaches. The critical conditions for the misfit dislocation generation are studied and discussed in detail with special attention to the non-classical surface/interface effect. It is shown that this effect is significant for fine cores of radius smaller than roughly 20 interatomic distances. The positive and negative surface/interface Lamé constants mostly make the generation of the misfit dislocation easier and harder, respectively. Moreover, the positive (negative) residual surface/interface tensions mostly make the generation of the misfit dislocation harder (easier). The formation of individual misfit dislocation is energetically more preferential in finer two-phase nanowires, while the formation of misfit dislocation dipole is more expectable in the coarser ones.     

The Percolation Transition for the Zero-Temperature Stochastic Ising Model on the Hexagonal Lattice

On the planar hexagonal lattice , we analyze the Markov process whose state (t), in , updates each site v asynchronously in continuous time t0, so that _v (t) agrees with a majority of its (three) neighbors. The initial _v (0)'s are i.i.d. with P[ _v (0)=+1]=p[0,1]. We study, both rigorously and by Monte Carlo simulation, the existence and nature of the percolation transition as t and p1/2. Denoting by ⁺(t,p) the expected size of the plus cluster containing the origin, we (1) prove that ⁺(,1/2)= and (2) study numerically critical exponents associated with the divergence of ⁺(,p) as p1/2. A detailed finite-size scaling analysis suggests that the exponents and of this t= (dependent) percolation model have the same values, 4/3 and 43/18, as standard two-dimensional independent percolation. We also present numerical evidence that the rate at which (t)() as t is exponential.     

Study on sound transmission characteristics of a cylindrical shell using analytical and experimental models

A circular cylindrical cavity enclosed by a thin elastic shell is found in many practical devices such as expansion volume mufflers, hermetic compressors and aircraft cabins. Analytical and experimental studies are conducted in this work to understand the characteristics of sound transmission through the cylindrical wall of such a system. Using an infinitely long circular cylindrical shell subjected to a plane incident wave, an exact solution is obtained by solving the classical shell vibration equations and the acoustic wave equations simultaneously. Transmission losses obtained from the solution are compared to the transmission losses that are measured for a cylindrical shell of finite length and the same cross-sectional dimensions. The comparison suggests that the theoretical model can be used as an effective design tool despite considerable simplifications involved.     

Angular dependence of the coercivity and remanence of ordered arrays of Co nanowires

The angular dependence of the coercivity and remanence of ordered hexagonal arrays of Co nanowires prepared using anodic aluminum oxide templates was investigated. The experimental evolution of coercivity as a function of the angle, in which the external field is applied, is interpreted considering micromagnetic simulations. Depending on the angle between the axis of the wire and the applied magnetic field direction our results show that the magnetization reversal mode changes from vortex to a transverse domain wall. Besides, we observed that the dipolar interactions cause a reduction in coercive fields, mainly in the direction of easy magnetization of the nanowires. Good agreement between numerical and experimental data is obtained.     

Reentrant phase transitions and multicompensation points in the mixed-spin Ising ferrimagnet on a decorated Bethe lattice

A mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration–iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin-1/2 Ising model on a simple (undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction and single-ion anisotropy on magnetic properties of the ferrimagnetic model is investigated in particular. It is shown that the total magnetization may exhibit multicompensation phenomenon and the critical temperature vs. the single-ion anisotropy dependence basically changes with the coordination number of the underlying Bethe lattice. The possibility of observing reentrant phase transitions is related to a high enough coordination number of the underlying Bethe lattice.