Superconducting and excitonic quantum phase transitions in doped Dirac electronic systems

We investigate the effect of superconducting and excitonic interactions, as well as their competition, on Dirac electrons on a bipartite planar lattice. It is shown that, at half-filling, Cooper pairs and excitons coexist if the superconducting and excitonic coupling parameters are equal and above a threshold corresponding to a quantum critical point. In the case where only the excitonic interaction is present, we obtain a critical chemical potential, as a function of the interaction strength. Conversely, if only the superconducting interaction is considered, we show that the superconducting gap displays a characteristic dome as charge carriers are doped into the system. We also show that, as the chemical potential increases, superconductivity tends to suppress the excitonic order parameter.     

A first-order level-2 phase transition in thermodynamic formalism

We show the existence of a phase transition at the level of measures for the generalized dimension of the maximal entropy measure in a model that was considered by F. Hofbauer and which is related to a model of M. Fisher. The model presented here is related to the one-dimensional Ising model in which a wall effect is assumed. In this situation, the problem has to be considered in the one-dimensional lattice . In general there is no first-order transition for the Ising model in the lattice , but under our assumptions such transitions can occur. The Ising model has the purpose of explaining the magnetization of ferromagnetic systems at low temperatures. The main difference of our result from a previous result of F. Hofbauer is that the transition is analyzed in the setting of the generalized dimension. This setting is more closely related to the observables. The main purpose of this paper is to explain another mathematical model for phase transition using the mathematical results obtained by F. Hofbauer. We also use results of the thermodynamic formalism in an essential way.     

Maps of intervals with indifferent fixed points: Thermodynamic formalism and phase transitions

We develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points. For such systems the formalism yields onedimensional systems with many-body infinite-range interactions for which the thermodynamics is well defined but Gibbs states are not. (Piecewise linear systems of this kind yield the soluble, in a sense, Fisher models.) We prove that such systems exhibit phase transitions, the order of which depends on the behavior at the indifferent fixed points. We obtain the critical exponent describing the singularity of the pressure and analyze the decay of correlations of the equilibrium states at all temperatures. Our technique relies on establishing and exploiting a relation between the transfer operators of the original map and its suitable (expanding) induced version. The technique allows one also to obtain a version of the Bowen-Ruelle formula for the Hausdorff dimension of repellers for maps with indifferent fixed points, and to generalize Fisher results to some nonsoluble models.Meyerhoff Visiting Professor, on leave from the Center for Transport Theory and Mathematical Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061.     

Superpositions of multifractals: Generators of phase transitions in the generalized thermodynamic formalism

We investigate the superposition of multifractals in the generalized thermodynamic formalism. It is shown analytically that phase transitions of first and second order are obtained and that the topology of the corresponding critical lines endows bicritical behavior. We demonstrate that these phase transitions can be observed in the spectrum of fractal dimensions and in the spectra of related quantities. Therefore, the obtained results are of importance for the interpretation of experimental systems.     

Comment on phase conventions in helicity formalism

Using the sequential decay process e<'+>e<'->→ J/ψ→ΛΛ, Λ→pπ<'->,Λ→pπ<'+> as an example, the procedure for deducing the full angular distribution is illustrated by adopting both the Jacob-Wick and Jackson conventions in the helicity formalism. To make sure that the final physical result is free of phase conventions, we point out that the coefficients that relate the angular momentum states in different coordinate systems of reference frames have to be taken into account properly in the procedure. The fact that those coefficients are constants suggests that the Jackson convention is favorable in dealing with the processes with sequential decays.     

Comment on phase conventions in helicity formalism

Using the sequential decay process m e⁺e^- → J/ψ → ΛΛ, Λ → pπ^-, Λ → pπ⁺ as an example, the procedure for deducing the full angular distribution is illustrated by adopting both the Jacob-Wick and Jackson conventions in the helicity formalism. To make sure that the final physical result is free of phase conventions, we point out that the coefficients that relate the angular momentum states in different coordinate systems of reference frames have to be taken into account properly in the procedure. The fact that those coefficients are constants suggests that the Jackson convention is favorable in dealing with the processes with sequential decays.     

Chiral phase transitions in quantum chromodynamics at finite temperature: Hard-thermal-loop resummed Dyson-Schwinger equation in the real time formalism

Chiral phase transition in thermal QCD is studied by using the Dyson-Schwinger (DS) equation in the real time hard thermal loop approximation. Our results on the critical temperature and the critical coupling are significantly different from those in the preceding analyses in the ladder DS equation, showing the importance of properly taking into account the essential thermal effects, namely the Landau damping and the unstable nature of thermal quasiparticles.     

Thermodynamic formalism of phase transitions in solid solutions

A thermodynamic theory of ferroelectric and ferroelectric-semiconductor solid solutions is presented with account of the effect of hydrostatic pressure in the cases of sharp as well as diffuse transitions. A number of analytical relations are obtained which allow to estimate the effect of admixture concentration and hydrostatic pressure on dielectric permeability, transition temperature, Curie-Weiss constant, heat capacity, thermal expansion coefficient and other properties of crystals with a ferroelectric subsystem. The theoretical results are compared with the experimental data.     

Metafluid dynamics and Hamilton-Jacobi formalism

Metafluid dynamics was investigated within Hamilton-Jacobi formalism and the existence of the hidden gauge symmetry was analyzed. The obtained results are in agreement with those of Faddeev-Jackiw approach.     

Picturing quantum phase transitions

We discuss the quantum phase transitions (QPT) in N-spin chains from the point of view of collective observables. We show that the measurement space representation is a convenient tool for the analysis of phase transitions, allowing the determination of an appropriate set of macroscopic order parameters (for a given Hamiltonian). Quantum correlations in the vicinity of the critical points are analyzed both in the ground states and low temperature thermal states.     

Commensurate incommensurate phase transitions

there are two types of Commensurate-Incommensurate Phase Transitions : t_I between the basic structure and the incommensurate phasis and t_L between the inc. phasis and the lock in phasis. They both have connected structures. So that, they must verify the relation between crystallographic groups in accordance with Landau's Theory. But we have to consider the three phases in the superspace - as we do at an ordered-disordered magnetic transition-because the inc. phasis ins't a crystal in the physical space; e.g., in order to cancel the “middle range order” of the inc. phasis at t_I, we are led to assume the grey (point) group to the basic structure in the superspace. Now both inc. phase and basic structure verify the connection between point-groups in the superspace in the same way as both para and ferro phases do at a ferroic transition in the physical space. We also show that the same type of relation is possible at t_L and we give the order parameter at both t_I and t_L.     

Coarsening in fluid phase transitions

We review the understanding of the kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected domains, based on overall composition in a binary liquid or on density in a vapor–liquid system, are discussed. Depending upon the morphology, various possible mechanisms for domain growth are pointed out and discussions of corresponding theoretical predictions are provided. On the computational front, useful models and simulation methodologies are presented. Theoretically predicted growth laws have been tested via molecular dynamics simulations of vapor–liquid transitions. In the case of a disconnected structure, the mechanism has been confirmed directly.     

Acoustic dispersion near structural phase transitions

We show on various examples, that elastic constant measurements provide a valuable tool for studying the dynamics of solids near phase transitions. Many experimental methods used in the investigation of phase transitions (NMR, neutron scattering, etc.) are able to give information on the dynamics, but in different regions of q- and ω-space, thereby probing different dynamical processes.

A comparison of the dynamics obtained from the elastic measurements with other techniques (NMR) demonstrates this very clearly for the cases of KSCN and C_60.     

Second order Hamiltonian formalism and constraints algebra for non-polynomial supergravities

The second order Hamiltonian formalism for a non-polynomial N = 1D = 10 supergravity coupled to super Yang-Mills theory is developed. This is done by starting from the first order canoncial covariant formalism on group manifold. The Hamiltonian, generator of time evolution, is found as a functional of the first class constraints of this coupled system. These contraints close the constraint algebra and they are the generators of all the Hamiltonian gauge symmetries.     

Absence of first-order phase transitions for antiferromagnetic systems

We consider a spin system with nearest-neighbor antiferromagnetic pair interactions in a two-dimensional lattice. We prove that the free energy of this system is differentiable with respect to the uniform external fieldh, for all temperatures and allh. This implies the absence of a first-order phase transition in this system.     

Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity

A phase-field system which describes the evolution of both the absolute temperature θ and the phase variable f during first-order transitions in thermal insulators is considered. A thermodynamic approach is developed by regarding the order parameter as a phase field and its evolution equation as a balance law. By virtue of the special form of the internal energy, a third-order nonlinearity appears in the energy balance in place of the (customarily constant) latent heat. As a consequence, the bounds 0≤f≤1 hold whenever θ is positive valued. In addition, a nonlinear Fourier law with conductivity proportional to temperature is assumed. Well-posedness for the resulting initial and boundary value problem are then established in a suitable setting.     

Kinetic equation approach to phase transitions

An exact mathematical discussion of the linearized Enskog-Vlasov equation is given. A criterion for the occurrence of the linear instability is related to a criterion for the occurrence of the bifurcation of the equilibrium stationary solution to the nonlinear Enskog-Vlasov equation. Mathematical results are interpreted physically in connection with phase transitions.     

Computer simulation studies of magnetic phase transitions

The advancements which have been made in the use of computer simulations to study magnetic-phase transitions and critical phenomena are reviewed. We describe how the use of a combination of sophisticated Monte Carlo simulation algorithms and reweighting (histogram) techniques have allowed the determination of the static critical behavior with unprecedented precision. The study of “dynamic” critical behavior in simple spin models by both Monte Carlo and spin dynamics methods is also reviewed. Recent estimates for dynamic critical exponents are given including those for true dynamics.