ON THE LOW-TEMPERATURE ORDERING OF THE 3D ATIFERROMAGNETIC THREE-STATE POTTS MODEL

The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using Monte Carlo simulations. The ordering in a medium temperature range below the critical point is investigated in detail. Two different regimes have been observed: The so-called broken sublattice-symmetry phase dominates at sufficiently low temperatures, while the phase just below the critical point is characterized by an effectively continuous order parameter and by a fully restored rotational symmetry. However, the later phase is not the permutationally sublattice symmetric phase recently predicted by the cluster variation method.Comment: 20 pages with 9 figures in a single postscript file (compressed and uuencoded by uufiles -gz -9) plus two big figures in postscript file

Fractal Measures of Sea, Lake, Strait, and Dam-Reserve Shores: Calculation, Differentiation, and Interpretation

The fractal dimensions d_f of the shore lines of the Mediterranean, the Aegean, the Black Sea, the Bosphorus Straits (on both the Asian and European sides), the Van Lake, and the lake formed by the Ataturk Dam have been calculated. Important distinctions have been found and explained.Comment: 3 pages, 2 figures, 1 tabl

Ordered phase and phase transitions in the three-dimensional generalized six-state clock model

We study the three-dimensional generalized six-state clock model at values of the energy parameters, at which the system is considered to have the same behavior as the stacked triangular antiferromagnetic Ising model and the three-state antiferromagnetic Potts model. First, we investigate ordered phases by using the Monte Carlo twist method (MCTM). We confirmed the existence of an incompletely ordered phase (IOP1) at intermediate temperature, besides the completely ordered phase (COP) at low-temperature. In this intermediate phase, two neighboring states of the six-state model mix, while one of them is selected in the low temperature phase. We examine the fluctuation the mixing rate of the two states in IOP1 and clarify that the mixing rate is very stable around 1:1. The high temperature phase transition is investigated by using non-equilibrium relaxation method (NERM). We estimate the critical exponents beta=0.34(1) and nu=0.66(4). These values are consistent with the 3D-XY universality class. The low temperature phase transition is found to be of first-order by using MCTM and the finite-size-scaling analysis

The Critical Properties of Two-dimensional Oscillator Arrays

We present a renormalization group study of two dimensional arrays of oscillators, with dissipative, short range interactions. We consider the case of non-identical oscillators, with distributed intrinsic frequencies within the array and study the steady-state properties of the system. In two dimensions no macroscopic mutual entrainment is found but, for identical oscillators, critical behavior of the Berezinskii-Kosterlitz-Thouless type is shown to be present. We then discuss the stability of (BKT) order in the physical case of distributed quenched random frequencies. In order to do that, we show how the steady-state dynamical properties of the two dimensional array of non-identical oscillators are related to the equilibrium properties of the XY model with quenched randomness, that has been already studied in the past. We propose a novel set of recursion relations to study this system within the Migdal Kadanoff renormalization group scheme, by mean of the discrete clock-state formulation. We compute the phase diagram in the presence of random dissipative coupling, at finite values of the clock state parameter. Possible experimental applications in two dimensional arrays of microelectromechanical oscillators are briefly suggested.Comment: Contribution to the conference "Viewing the World through Spin Glasses" in honour of Professor David Sherrington on the occasion of his 65th birthda

Directed paths on hierarchical lattices with random sign weights

We study sums of directed paths on a hierarchical lattice where each bond has either a positive or negative sign with a probability $p$. Such path sums $J$ have been used to model interference effects by hopping electrons in the strongly localized regime. The advantage of hierarchical lattices is that they include path crossings, ignored by mean field approaches, while still permitting analytical treatment. Here, we perform a scaling analysis of the controversial ``sign transition'' using Monte Carlo sampling, and conclude that the transition exists and is second order. Furthermore, we make use of exact moment recursion relations to find that the moments always determine, uniquely, the probability distribution $P(J)$. We also derive, exactly, the moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations ($n\to 0$) to obtain for odd and even moments yield a new signal for the transition that coincides with Monte Carlo simulations. Analysis of high moments yield interesting ``solitonic'' structures that propagate as a function of $p$. Finally, we derive the exact probability distribution for path sums $J$ up to length L=64 for all sign probabilities.Comment: 20 pages, 12 figure

Dynamic phase transition properties and hysteretic behavior of a ferrimagnetic core-shell nanoparticle in the presence of a time dependent magnetic field

We have presented dynamic phase transition features and stationary-state behavior of a ferrimagnetic small nanoparticle system with a core-shell structure. By means of detailed Monte Carlo simulations, a complete picture of the phase diagrams and magnetization profiles have been presented and the conditions for the occurrence of a compensation point $T_{comp}$ in the system have been investigated. According to N\'{e}el nomenclature, the magnetization curves of the particle have been found to obey P-type, N-type and Q-type classification schemes under certain conditions. Much effort has been devoted to investigation of hysteretic response of the particle and we observed the existence of triple hysteresis loop behavior which originates from the existence of a weak ferromagnetic core coupling $J_{c}/J_{sh}$, as well as a strong antiferromagnetic interface exchange interaction $J_{int}/J_{sh}$. Most of the calculations have been performed for a particle in the presence of oscillating fields of very high frequencies and high amplitudes in comparison with exchange interactions which resembles a magnetic system under the influence of ultrafast switching fields. Particular attention has also been paid on the influence of the particle size on the thermal and magnetic properties, as well as magnetic features such as coercivity, remanence and compensation temperature of the particle. We have found that in the presence of ultrafast switching fields, the particle may exhibit a dynamic phase transition from paramagnetic to a dynamically ordered phase with increasing ferromagnetic shell thickness.Comment: 12 pages, 12 figure

On the low-temperature phase of the three-state antiferromagnetic Potts model on the simple cubic lattice

The three-state antiferromagnetic Potts model on the simple cubic lattice is investigated using the cluster variation method in the cube and the star-cube approximations. The broken-sublattice-symmetry phase is found to be stable in the whole low-temperature region, contrary to previous results obtained using a modified cluster variation method. The tiny free energy difference between the broken-sublattice-symmetry and the permutationally-symmetric-sublattices phases is calculated in the two approximations and turns out to be smaller in the (more accurate) star-cube approximation than in the cube one.Comment: 4 pages REVTeX + 2 PostScript figures, to be published in Phys. Rev. E as a Rapid Communicatio

Effect of Preform Thickness and Volume Fraction on Injection Pressure and Mechanical Properties of Resin Transfer Molded Composites

An experimental study is performed to characterize the effect of the thickness of random preforms on injection pressure and mechanical properties of resin transfer molded (RTM) parts. Center-gated, disk-shaped parts are molded using two different chopped-strand glass fiber preforms. Both preforms have random microstructure but different planar densities (i.e., different uncompressed layer thicknesses). Tensile strength, short-beam shear strength, and elastic modulus are measured for parts molded with each preform type at three different fiber volume fractions of 6.84, 15.55, and 24.83%. Although mechanical properties are found to increase linearly with volume fraction, significant difference is not observed between disks containing thick and thin mats at equivalent fiber volume fraction.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Inhomogeneity-induced second-order phase transitions in Potts model on hierarchical lattices

The thermodynamics of the $q$-state Potts model with arbitrary $q$ on a class of hierarchical lattices is considered. Contrary to the case of the crystal lattices, it has always the second-order phase transitions. The analytical expressions fo the critical indexes are obtained, their dependencies on the structural lattice pararmeters are studied and the scailing relations among them are establised. The structural criterion of the inhomogeneity-induced transformation of the transition order is suggested. The application of the results to a description of critical phenomena in the dilute crystals and substances confined in porous media is discussed.Comment: 9 pages, 2 figure

Sine-Gordon mean field theory of a Coulomb Gas

Sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean field free energy is constructed and the corresponding phase diagrams in two (2d) and three dimensions (3d) are obtained. When analyzed in terms of chemical potential, the Sine-Gordon theory predicts the phase diagram topologically identical with the Monte Carlo simulations and a recently developed Debye-H\"uckel-Bjerrum (DHBj) theory. In 2d we find that the infinite order Kosterlitz-Thouless line terminates in a tricritical point, after which the metal-insulator transition becomes first order. However, when the transformation from chemical potential to the density is made the whole of the insulating phase is mapped onto zero density.Comment: 5 pages, Revtex with twocolumn style, 2 Postscript figures. Submitted to PR