Order-disorder phase transition in a cliquey social network

We investigate the network model of community by Watts, Dodds and Newman (D.J. Watts et al., Science 296, 1302 (2002)) as a hierarchy of groups, each of 5 individuals. A homophily parameter α controls the probability proportional to exp (-αx) of selection of neighbours against distance x. The network nodes are endowed with spin-like variables s_i = ± 1, with Ising interaction J > 0. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature T_c is close to 3.8 for α < 0.0 and it falls down to zero above this value. The result provides a mathematical illustration of the social ability to a collective action via weak ties, as discussed by Granovetter in 1973.     

Order-disorder phase transition in CoPd thin films

The thin films of a CoPd alloy in the equiatomic composition region are prepared by condensation at different substrate temperatures. The substrate temperature is varied from the liquid nitrogen temperature to +280°C. At low substrate temperatures, the crystal structure of the condensed films is the single-crystal blocks of the hexagonal close-packed (hcp) phase. As the substrate temperature is further increased, the domains characterized in the initial state by the microdiffraction patterns in the form of a diffuse halo appear in the films, and these domains have a clear-cut boundary with the regions indicated by point reflections in the electron diffraction patterns. At substrate temperatures from +150 to 160°C, the CoPd alloy films in the equiatomic composition region are fully amorphous. The given state is a polymorphic transformation of the martensitic type. It arises in the martensitic transformation of the low-temperature hcp phase to the high-temperature fcc phase. Original Russian Text ? E.M. Artem’ev, M.E. Artem’ev, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 11, pp. 838–840.     

Order-disorder phase transition in CoPd thin films

The thin films of a CoPd alloy in the equiatomic composition region are prepared by condensation at different substrate temperatures. The substrate temperature is varied from the liquid nitrogen temperature to +280°C. At low substrate temperatures, the crystal structure of the condensed films is the single-crystal blocks of the hexagonal close-packed (hcp) phase. As the substrate temperature is further increased, the domains characterized in the initial state by the microdiffraction patterns in the form of a diffuse halo appear in the films, and these domains have a clear-cut boundary with the regions indicated by point reflections in the electron diffraction patterns. At substrate temperatures from +150 to 160°C, the CoPd alloy films in the equiatomic composition region are fully amorphous. The given state is a polymorphic transformation of the martensitic type. It arises in the martensitic transformation of the low-temperature hcp phase to the high-temperature fcc phase.     

Order-disorder transition in a system of magnetic holes

Polystyrene spheres of the same size (10–100μm) dispersed in ferrofluid produce voids, which have been denoted magnetic holes. A two-dimensional system of interacting magnetic holes confined between two glass plates and subject to rotating magnetic fields in the sample plane are studied in a light microscope. For low frequencies of the field rotation, the holes form pairs, which arrange themselves in a regular triangular lattice when stabilized with a weak constant field normal to the sample plane. By increasing the frequency of the rotating field, we observe that above a critical frequency, the steady forward rotation of the pairs is interrupted by backward rotations in short time intervals. Because the intervals of backward rotation occur at different times for each individual pair, disorder is introduced in the system, and the triangular lattice of pairs “melts” and forms a liquid-like structure at high rotation frequencies of the field. This “melting” transition is observed both directly and in light scattering experiments using a laser.     

Order-disorder phase transition in Ni4W alloy

The order-disorder phase transition in Ni₄W alloy with a D1 _a superlattice was studied experimentally by x-ray structural analysis and theoretically by the Green function method. An experimental temperature dependence was obtained for the equilibrium parameter of long-range order for Ni₄W alloy. It was established that the order-disorder phase transition in the alloy is a first-order transition; the transition occurs through the two-phase region D1_a + A1. The Green function technique, with account for the pair-correlation functions, was used to describe the order-disorder transition for the D1 _a superlattice. The theoretical temperature dependence obtained for the equilibrium parameter of long-range order is in satisfactory agreement with the experimental curve.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 92–97, April, 1978.     

Order-disorder transition in the solid phase of a charged hard sphere model

We investigate the solid phases of the restricted primitive model (RPM). Monte Carlo simulations show the existence of an order-disorder transition from a substitutionally disordered face centered cubic lattice (fcc) to a new ordered fcc structure which is proposed as the ground state of the RPM at the close packing density. Our results suggest that the new phase might turn out in a new triple point in the RPM phase diagram involving three solid phases: CsCl, fcc ordered and fcc disordered structures. The order-disorder transition is also studied using the cell theory. The theory shows good agreement with the simulation results and suggests that the transition is weakly first order.     

Order-disorder transition in one-dimensional system with disorder in composition

The influence of structural inhomogeneity onto order-disorder transitions in 1D systems is considered in the scope of the Potts-like model with many-particle interactions. The helix-coil transition in DNAs, heterogeneous by hydrogen bonding energy, is considered as an example. The microcanonical method is employed to evaluate the free energy. The secular equation for the heteropolymer is constructed. Both the melting temperature and interval of DNA melting are obtained. In the limit of small difference between inverse melting temperatures of poly(A-T) and poly(G-C), the coincidence with classical results is obtained.     

Order-disorder component in the phase transition mechanism of 18O enriched strontium titanate

Ti and Sr nuclear magnetic resonance spectra of 18O enriched SrTiO3 (STO-18) provide direct evidence for Ti disorder already in the cubic phase and show that the ferroelectric transition at T(C)=24 K occurs in two steps. Below 70 K rhombohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below T(C). This shows that the elusive ferroelectric transition in STO-18 is indeed connected with local symmetry lowering and implies the existence of an order-disorder component in addition to the displacive soft mode one. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric state of STO-16 as well. The concentration of the rhombohedral clusters is, however, not high enough to allow for percolation.     

Order-disorder phase transition in ZrV2D3.6

The deuterated C15-type Laves phase ZrV₂D_3.6 undergoes a structural phase transition near room temperature (T ≈ 325 K). In the cubic high-temperature phase the deuterium atoms are disordered over two types of tetrahedral interstices, the centres of which are 1.3 Å apart. In the tetragonal low-temperature phase the D atoms are ordered and occupy only the energetically more favourable interstices. The tetragonal structure is isotypic with the low-temperature phase of HfV₂D₄. The shortest D—D distance is 2.1 Å.     

Order-disorder transition in nanoscopic semiconductor quantum rings

Using the path integral Monte Carlo technique we show that semiconductor quantum rings with up to six electrons exhibit a temperature, ring diameter, and particle number dependent transition between spin ordered and disordered Wigner crystals. Because of the small number of particles the transition extends over a broad temperature range and is clearly identifiable from the electron pair correlation functions.     

Melt-crystal phase transition in a two-component system

The melt-crystal phase transition in a two-component system is described by a generalized Ornstein-Zernicke equation for one- and two-particle distribution functions. The jump in the density δn under melt crystallization is a small parameter. The desired distribution functions are found as δn power series. The two-particle distribution function for the melt along its crystallization line is chosen as a zeroth approximation. Institute of Applied Physics at the Irkutsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 54–61, February 2000.     

Order-disorder transition for corrugated Au layers

Atomic-scale structure of the growth of a gold film on (1 1 2) plane of Mo single crystal was investigated by means of low energy electron diffraction (LEED) and scanning tunneling microscopy (STM) up to two monolayers (ML) of gold coverage. Both LEED and STM results establish that Au grows on Mo(1 1 2) in a layer-by-layer mode, for at least the first two monolayers. A number of ordered structures are formed and both the first and second layers adopt the Mo(1 1 2) 1 × 1 surface structure upon completion. For some gold layers on Mo(1 1 2), notably the 1.66 monolayer 3 × 1 and 1.75 monolayer 4 × 1 gold overlayers, we find evidence of a phase transition associated with increasing disorder in gold layers with structural corrugation and anisotropic band structure. The signature of this phase transition, at temperatures in the range of 400-500 K, is a sharp decrease in the overlayer effective Debye temperature.     

Role of multistability in the transition to chaotic phase synchronization

In this paper we describe the transition to phase synchronization for systems of coupled nonlinear oscillators that individually follow the Feigenbaum route to chaos. A nested structure of phase synchronized regions of different attractor families is observed. With this structure, the transition to nonsynchronous behavior is determined by the loss of stability for the most stable synchronous mode. It is shown that the appearance of hyperchaos and the transition from lag synchronization to phase synchronization are related to the merging of chaotic attractors from different families. Numerical examples using Rossler systems and model maps are given. (c) 1999 American Institute of Physics.     

Photoinduced semiconductor-metal phase transition in a peierls system

The dynamical equation for the order parameter of the metal-semiconductor phase transition, as well as the kinetic equation for the density of nonequilibrium electron-hole pairs of a Peierls system in a light field, has been derived. An expression for the time τ of the nonthermal photoinduced semiconductor-metal phase transition has been obtained from these equations for the case of an ultrashort light pulse. It has been shown that, to initiate the phase transition, the energy density W of the light pulse must be higher than the critical value W _c. The W _c, τ, and optical absorption coefficient γ₀ that are calculated in the framework of the proposed model are in agreement with the experimental data (W _c ≈ 12 mJ/cm², τ ≈ 75 fs, and γ₀ ≈ 10⁵ cm^?1) on the irradiation of a vanadium dioxide film by a laser pulse with a duration of τ_p ≈ 15 fs, a photon energy of ?θ₀ = 1.6 eV, and an energy density of W = 50 mJ/cm².     

Infinite-order phase transition in a classical spin system

For an exactly soluble classical spin model with long-range inhomogeneous coupling it is proved that in the absence of external magnetic field the free energy is aC function of the temperature at the critical point.