Renormalization Group Analysis of the Self-Avoiding Paths on the d-Dimensional Sierpiński Gaskets

Notion of the renormalization group dynamical system, the self-avoiding fixed point and the critical trajectory are mathematically defined for the set of self-avoiding walks on the d-dimensional pre-Sierpiski gaskets (n-simplex lattices), such that their existence imply the asymptotic behaviors of the self-avoiding walks, such as the existence of the limit distributions of the scaled path lengths of canonical ensemble, the connectivity constant (exponential growth of path numbers with respect to the length), and the exponent for mean square displacement. We apply the so defined framework to prove these asymptotic behaviors of the restricted self-avoiding walks on the 4-dimensional pre-Sierpiski gasket.     

The anisotropic quantum antiferromagnet on the Sierpiński gasket: Ground state and thermodynamics

We investigate an antiferromagnetic s = 1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpiski gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to a the Sierpiski gasket with N = 42. Using this and other methods we calculate ground state energies, spin gap, spin-spin correlations and specific heat data and conclude that the s = 1/2 quantum antiferromagnet on the Sierpinski gasket shows a disordered magnetic ground state with on the Sierpinski gasket shows a disordered magnetic ground state with a very short correlation length of and an, albeit very small, spin gap. This conclusion holds for Heisenberg as well a for XY exchange.Received: 18 February 2004, Published online: 20 April 2004PACS: 75.10.-b General theory and models of magnetic ordering - 05.45.Df Fractals - 75.40.Mg Numerical simulation studies     

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpiński gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with 0 ≤ J_b/J_a< 1, and an interesting crossover behavior between different phases at J_b/J_a = 1 is unveiled, whose dynamics can be described by the J_b/J_a-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpiński gasket are obtained in both the 1 / 3 plateau disordered phase and the 5/9 plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpiński gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.     

Chaotic properties of multipoint correlation functions of an Ising model with long-range interactions on the Sierpiński—Gasket lattice

A class of multispin correlation functions of an Ising model with ferromagnetic nearest neighbor interactionsK and constant (distance-independent) long-range interactionsQ ₁=Q,l=1,2,..., on the Sierpiski-gasket lattice is considered. Using an exact method for calculating thermodynamic functions of hierarchically constructed Ising systems, it is shown that, for a set of values ofQ and for almost all values ofK, someM _k-spin correlation functions, whereM _k=3 ^k +3 withk=1,2,...,n andn=1,2,... being the order of lattice construction, change chaotically asn, k, and therebyM _k increase to infinity. Accordingly, in the thermodynamic limit, these correlation functions prove to be nonanalytic for appropriate values ofQ andK. SinceM _k-point correlation functions withk being finite, i.e., correlation functions involving finite numbers of spins, remain analytic asn tends to infinity, there is a smooth crossover between analytic properties of correlation functions of the two types.     

The pressure-induced phase transition of the solid β–HMX

The structural, vibrational and thermodynamic properties of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β–HMX) crystal have been studied using the isothermal-isobaric molecular dynamics (NPT-MD) simulations. The variations of cell volume, lattice constants and molecular geometry of solid β–HMX are presented and discussed at different pressure and temperature. It was found that the N–N bond is significantly lengthened with increasing temperature, which suggests that it is relevant to the initial decomposition. An abrupt change at 27 Gpa for the volume and internal geometrical parameters was observed. This is in good accord with the experimental observation that there is a phase transition at 27 GPa, which is clearly due to conformational change, not chemical reaction. The vibrational frequencies at ambient conditions agree well with experimental results, and the pressure/temperature-induced frequency shifts of these modes are discussed. Frequency discontinuity was also observed at pressure when the phase transition occurred. The Grüneisen parameter was obtained using the vibrational frequency.     

Elasticity of the B2 phase and the effect of the B1–B2 phase transition on the elasticity of MgO

A study of the high-pressure anisotropy of MgO was conducted using first-principles calculations based on density functional theory within the generalized gradient approximations. The pressure dependence of the elastic stiffness coefficients and the anisotropy parameters, in both B1 and B2 phases, shows that for high-hydrostatic compression the easiest deformation is the shear along (100) plane and the the material's response to deformation and to shearing strains is quite the same. According to the calculations of the velocities of propagation of elastic waves, we deduced that MgO develop an elastic anisotropy, especially, in the B1 phase. We present the B2 phase elastic properties which are not already studied under high pressure.     

The meaning of the terms “phase” and “phase transition”

Various meanings of the terms phase and phase transition encountered in scientific literature are discussed. These terms supplement each other and cover only together all the macroscopic situations which are now denoted by this term.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 67–71, August, 1988.     

The mass effect of the quark phase transition in supernova core

Constituent quark mass model is adopted as a tentative one to study the phase transition between two-flavour quark matter and more stable three-flavour quark matter in the core of supernovae. The result shows that the transition has a significant influence on the increasing of the core temperature, the neutrino abundance and the neutrino energies, which contributes to the enhancement of the successful probability of supernova explosion. However, the equilibrium values of these parameters （except the temperature） from the constituent quark mass model in this work are slightly bigger than those obtained from the other model. And we find that the constituent quark mass model is also applicable to describing the transition in the supernova core.     

Study on the mechanism of phase transition and embrittlement for γ-Fe by hydrogen with stress through the first principles method

Because of the influence of hydrogen and the stress corrosion cracking, the damage of metal is quite frequent. It leads to dangerous failures, the loss of property as well as large compensational payments for insurance companies. However, the issue of the precise role of hydrogen in the process is unclear and the mechanism is not available. Based on the binding energy analysis, it was found that H prefers octahedral-like positions for γ-Fe, and could enhance the stability of structure with dissolving into γ-Fe. The higher the concentration of H, the much more remarkable the observation is. Therefore, H is easily soluble in γ-Fe. Under the applied tensile stress, γ-Fe and H doped γ-Fe undergo the stages of elastic and plastic deformations. Meanwhile, H induces γ-Fe phase transition.This process starts from the atomic layer adjacent to H, then gradually extends far. As a consequence, the intergranular embrittlement and cracking happened.     

The mean field model with P2θ2 coupling for the smectic A-smectic C* phase transition in liquid crystals

Using mean field theory with a P²θ² coupling term in the free energy expansion, we calculate the polarization as a function of temperature for the smectic A-smectic C* phase transition in a liquid crystalline material. Our calculated polarization values are in good agreement with the experimental data.     

On the nature of the phase transition triggered by vortex-like defects in the 2D Ginzburg–Landau model

The two-dimensional lattice Ginzburg–Landau Hamiltonian is simulated numerically for different values of the coherence length ξ in units of the lattice spacing a, a parameter which controls amplitude fluctuations. The phase diagram on the plane T–ξ is measured. Amplitude fluctuations change dramatically the nature of the phase transition: for values of ξ/a≃1, instead of the smooth Kosterlitz–Thouless transition there is a first-order transition with a discontinuity in the vortex density v and a sharper drop in the helicity modulus Γ. Both observables v and Γ are analyzed in detail at the crossover region between first and second order which occurs for intermediate values of ξ/a.     

The connection of the nuclear “Coriolis” force with classical mechanics

The relation between the socalled Coriolis couplingI · j, operating in rotating nuclei, and the classical Coriolis force is discussed. The system forces acting in the cranking model for non-uniform rotation and in the rotator-particle model are examined. Differences with the molecular Coriolis coupling are indicated.     

The connection of the nuclear “Coriolis” force with classical mechanics

The relation between the socalled Coriolis couplingI · j, operating in rotating nuclei, and the classical Coriolis force is discussed. The system forces acting in the cranking model for non-uniform rotation and in the rotator-particle model are examined. Differences with the molecular Coriolis coupling are indicated.     

Influence of shifted phase value on the output spectra of DFB lasers with phase shifter

DFB lasers with π/2 phase shifter can run stably on single mode and providevery high side mode suppression ratio (MSR). This attractive feature may be degraded ifphase shift deviates from π/2. In this paper, we analyze theoretically how the output spectraand side mode suppression ratio are influenced by the deviation value of phase shift from π/2.     

Effect of density variation on the Sm A–I phase transition properties

Based on a thermodynamic model, we investigate how the density variation influences the smectic (Sm A)–isotropic (I) phase transition. We find that the density variation shifts the smectic A–isotropic transition temperature, however, first-order nature of the transition remains the same. Here, we also examine the effect of high pressure on the thermodynamic quantities. The present analysis shows that the pressure strongly influences the enthalpy and density step at the clearing transition. The pressure dependence of the thermodynamic properties is incorporated through the pressure dependent second Landau coefficient and the coefficients which couple the nematic and smectic order parameters to the density. We find a close agreement between theoretical and experimental results. Furthermore, we discuss the implications of the results for achiral liquid crystals.     

On the ferroelectric phase transition in polytypes of β-TlInS2 crystals

Permittivity measurements and x-ray diffraction study were performed for polytypes c and 2c of β-TlInS₂ crystals in the temperature range T = 160–250 K. Substantial differences are revealed in the temperature, sequence, and character of the structural phase transitions associated with the formation of incommensurate modulated structures and the occurrence of a ferroelectric state in these polytypes.