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A large-scale Monte Carlo calculation is presented of the deconfining phase-transition temperature in lattice quantum chromodynamics without fermions. By using the Wilson action, it is found that the transition temperature as a function of the lattice coupling g is consistent with scaling behavior dictated by the perturbative beta function for 6/g-squared greater than 6.15.
It is demonstrated from first principles how the existence of string-like structures can cause a system to undergo a phase transition. In particular, the role of topologically stable cosmic string in the restoration of spontaneously broken symmetries is emphasized. How the thermodynamic properties of strings alter when stiffness and nearest neighbor string-string interactions are included is discussed.
A linearized version of the Hartree-Fock method is used as a probe to investigate phase transitions in fermionic systems with many-body interactions. An application to a new exactly solvable model which includes two- and three-body forces is shown.
The statistical mechanics of a system of semiflexible chains, which can represent polymer liquid crystals, long-chain biomolecules, stiff wormlike micelles, or columns of discotic liquid crystals, are examined. A continuum theory is used to calculate static correlation functions in the hexagonal and nematic phases. Two correlation functions are considered: (1) the structure factor which describes fluctuations in the density; and (2) the director fluctuation spectrum, which describes fluctuations in the local optical axis. In addition, a model is developed for the phase transitions of a system of infinitely long, semiflexible chains which interact through a steric, excluded-volume repulsion. The model yields generic phase diagrams in terms of pressure or density vs. persistence length or temperature.
A calculation that minimizes the energy of solid N2 with respect to a rhombohedral distortion of the Pm 3n structure shows that a low-temperature phase transition occurs into the R 3c calcite structure at P = 19.2 kbar with a volume change of 0.125 cu cm/mole. This transition agrees with recent Raman scattering measurements. Another transition from R 3c into R3(bar)m is predicted at P = 67.5 kbar, with a volume change of 0.1 cu cm/mole. The pressure dependence of the intramolecular mode frequencies for the R 3c structure are in reasonably good agreement with the two main branches observed experimentally.
A review of the formation of large scale structure through gravitational growth of primordial perturbations is given. This is followed by a discussion of how symmetry breaking phase transitions in the early universe might have produced the required perturbations, in particular through the formation and evolution of a network of cosmic strings. Finally, the statistical mechanics of string networks, for both cosmic and fundamental strings is discussed, leading to some more speculative ideas on the possible role of fundamental strings (superstrings or heterotic strings) in the very early universe.
A review of the formation of large scale structure through gravitational growth of primordial perturbations is given. This is followed by a discussion of how symmetry breaking phase transitions in the early universe might have produced the required perturbations, in particular through the formation and evolution of a network of cosmic strings.
An exact analysis of the Ising model with infinite-range interactions in a random field and a local mean-field theory in three dimensions is carried out leading to a phase diagram with several coexistence surfaces and lines of critical points. The results show that the phase diagram depends crucially on whether the distribution of random fields is symmetric or not. Thus, Ising-like phase transitions in a porous medium (the asymmetric case) are in a different universality class from the conventional random-field model (symmetric case).
After presenting the current view of the processes taking place during the cosmological transition from 'quark soup' to normal hadron matter, attention is given to what happens to cosmological nucleosynthesis in the presence of small-scale baryon inhomogeneities. The QCD phase transition is among the plausible sources of this inhomogeneity. It is concluded that the formation of primordial 'quark nuggets' and other cold exotica requires very low entropy regions at the outset, and that even the more modest nonlinearities perturbing nucleosynthesis probably require some ingredient in addition to a quiescent, mildly supercooled transition.
Pure fluids and fluid mixtures near critical points are identified and are related to the progress of several disciplines. Consideration is given to thermodynamic properties, transport properties, and the complex nonlinear phenomena which occur when fluids undergo phase transitions in the critical region. The distinction is made between practical limits which may be extended by advances in technology and intrinsic ones which arise from the modification of fluid properties by the earth's gravitational field. The kinds of experiments near critical points which could best exploit the low gravity environment of an orbiting laboratory are identified. These include studies of the index of refraction, constant volume specific heat, and phase separation.
A new model equation of state is applied, based on realistic interparticle potentials and a self-consistent treatment of the internal levels, to fluid hydrogen at high density. This model shows a strong connection between molecular dissociation and pressure ionization. The possibility of a first-order plasma phase transition is considered, and for which both the evolution in temperature and the critical point is given.
Model weak D-type ionization fronts have been constructed which include the effects of magnetic pressure and H I coolants. Ly-alpha cooling is found to suppress the high-temperature peak of 15,000 to 20,000 K found in earlier models. Ionization fronts are found to be closely related to phase transitions.
Basis invariant characterizations of bound states and bound fraction of a partially ionized hydrogen plasma are given in terms of properties of the spectrum of eigenvalues and eigenfunctions of the equilibrium quantum statistical one-proton-one-electron reduced density matrix. It is suggested that these can be used to place theories of a proposed plasma-ionization phase transition on a firm foundation. This general approach may be relevant to cosmological questions such as the quark deconfinement-confinement transition.
The main features of the theory of line groups, and their irreducible representations are briefly discussed, as well as the most important applications of them. A new approach in the general symmetry analysis of the modulated systems is presented. It is shown, that the line group formalism could be a very effective tool in the examination of the structural phase transitions in High Temperature SUperconductors. As an example, the material YBa2Cu3O(7-x) is discussed briefly.
It was argued, and fought through numerical work that the results of non-dynamical Monte Carlo computer simulations cannot be applied to describe the formation of topological defects when the correlation length at the Ginzburg temperature is significantly smaller than the horizon size. To test the current hypothesis that infinite strings at formation are essentially described by Brownian walks of size the correlation length at the Ginzburg temperature, fields at the Ginzburg temperature were equilibrated. Infinite structure do not exist in equilibrium for reasonable definitions of the Ginzburg temperature, and horizons must be included in a proper treatment. A phase transition, from small-scale to large-scale string or domain wall structure, is found to occur very close to the Ginzburg temperature, in agreement with recent work. The formation process of domain walls and global strings were investigated through the breaking of initially ordered states. To mimic conditions in the early Universe, cooling times are chosen so that horizons exist in the sample volume when topological structure formation occurs. The classical fields are evolved in real-time by the numerical solution of Langevin equations of motion on a three dimensional spatial lattice. The results indicate that it is possible for most of the string energy to be in small loops, rather than in long strings, at formation.
An analytic model based on a second-order accurate global virial analysis is used to describe two stable equilibrium states for rotating gas clouds: a pressure-supported, diffuse state and a rotationally supported, compact state. Diffuse and compact equilibrium sequences are identified along which slow, secular evolution of a gas cloud can occur. A virial analysis provides analytic expressions for the limiting masses of gas clouds at points of dynamical instability. The minimum mass below which external triggers of any amplitude cannot effectively induce star formation is identified for adiabatic gas clouds. It is suggested that fluctuations in the ISM of some galaxies may actually cause star formation to proceed primarily via a phase transition, rather than via the classical Jeans instability.
Preliminary results are reported for an investigation comparing theoretical models of the sudden appearance of an extended RGB (and its effects on the spectral energy distributions of stellar populations) with data from ESO CCD observations of clusters in the LMC and SMC. Isochrones for the entire RGB are being constructed on the basis of 100 new evolutionary sequences (calculated using the evolution code of Sweigart and Gross, 1976 and 1978) to permit determination of synthetic colors and spectral energy distributions. The observations so far indicate a main sequence about 0.1 mag redder than that predicted by the present models or by the isochrones of VandenBerg and Bell (1985), and fail to show a B-V color difference at the RGB phase transition.
The thermodynamic properties of (CO2)N molecular aggregates of size N between 2 and 13 have been investigated. These crystallites exhibit well defined orientational order-disorder rotational transitions accompanied by a structural transition into a plastic crystallite phase. In addition, they exhibit melting and disassociation transitions. It is shown that the interpretation of experimental data, based upon dimer properties, depends crucially on these results. Equilibrium structures and orientations are also given.