Coulombic Phase Transitions in Dense Plasmas

We give a survey on the predictions of Coulombic phase transitions in dense plasmas (PPT) and derive several new results on the properties of these transitions. In particular we discuss several types of the critical point and the spinodal curves of quantum Coulombic systems. We construct a simple theoretical model which shows (in dependence on the parameter values) either one alkali-type transition (Coulombic and van der Waals forces determine the critical point) or one Coulombic transition and another van der Waals transition. We investigate the conditions to find separate Van der Waals and Coulomb transitions in one system (typical for hydrogen and noble gas-type plasmas). The separated Coulombic transitions which are strongly influenced by quantum effects are the hypothetical PPT, they are in full analogy to the known Coulombic transitions in classical ionic systems. Finally we give a discussion of several numerical and experimental results referring to the PPT in high pressure plasmas.     

Phase Transitions and Topology Changes in Configuration Space

The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant (the Euler characteristic) of certain submanifolds in the configuration space of two physical models. The models are the mean-field XY model and the one-dimensional XY model with nearest-neighbor interactions. The former model undergoes a second-order phase transition at a finite critical temperature while the latter has no phase transitions. The computation of this topologic invariant is performed within the framework of Morse theory. In both models topology changes in configuration space are present as the potential energy is varied; however, in the mean-field model there is a particularly strong topology change, corresponding to a big jump in the Euler characteristic, connected with the phase transition, which is absent in the one-dimensional model with no phase transition. The comparison between the two models has two major consequences: (i) it lends new and strong support to a recently proposed topological approach to the study of phase transitions; (ii) it allows us to conjecture which particular topology changes could entail a phase transition in general. We also discuss a simplified illustrative model of the topology changes connected to phase transitions using of two-dimensional surfaces, and a possible direct connection between topological invariants and thermodynamic quantities.     

Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates

Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the ``transitional gap'' are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria.     

Transitions to electrochemical turbulence

We report experimental evidence of transitions from limit cycle oscillations through a phase turbulent regime to space-time defect turbulence in a spatially (quasi-)one-dimensional electrochemical system with nonlocal coupling. The transitions are characterized in terms of the defect density, the Karhunen-Loève decomposition dimension, and a measure of the degree of spatial correlation in the data. Furthermore, these quantities give the first experimental confirmation that the spatial coupling range in electrochemical systems indeed depends on the distance between the working and the counterelectrode.     

Entropy majorization, thermal adiabatic theorem, and quantum phase transitions

Let a general quantum many-body system at a low temperature adiabatically cross through the vicinity of the system’s quantum critical point. We show that the system’s temperature is significantly suppressed due to both the entropy majorization theorem in quantum information science and the entropy conservation law in reversible adiabatic processes. We take the one-dimensional transverse-field Ising model and the spinless fermion system as concrete examples to show that the inverse temperature might become divergent around the systems’ critical points. Since the temperature is a measurable quantity in experiments, it can be used, via reversible adiabatic processes at low temperatures, to detect quantum phase transitions in the perspectives of quantum information science and quantum statistical mechanics.     

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.     

First-order transitions in one-dimensional systems with local couplings

We point out the existence of first-order phase transitions in a family of one-dimensional classical spin systems. The relevant features of such models are that they involve only local (but complex) interactions and that the corresponding transfer matrices are self-adjoint operators. Moreover, for a wide range of coupling parameters the models satisfy the reflection positivity condition. The generalization for continuous spin systems enjoys similar properties.     

Topology and Phase Transitions: The Case of the Short Range Spherical Model

We characterize the topology of the phase space of the Berlin-Kac spherical model in the context of the so called Topological Hypothesis, for spins lying in hypercubic lattices of dimension d. For zero external field we are able to characterize the topology exactly, up to homology. We find that, even though there is a continuum of changes in the topology of the corresponding manifolds, for d ≥ 3 there are abrupt discontinuities in some topological functions that could be good candidates to associate with the phase transitions that occur at the thermodynamic level. We show however that these changes do not coincide with the phase transitions and conversely, that no topological discontinuity can be associated to the points where the phase transitions take place. At variance with what happens in the Mean Field version of this same model, we show that these abrupt topological changes are accessible thermodynamically. We conclude that, even in short range systems, the topological mechanism does not seem to be responsible for the triggering of a phase transition. We also analyze the case of spins connected to a macroscopic number of (but not all) neighbors, and find that, similar to the results found for the fully connected version, in this case the topological hypothesis seems to hold: the phase transition coincides with an accumulation point of the topological changes present in configuration space. The question of the ensemble equivalence in the short range spherical model is also considered.     

Exact energy spectrum for models with equally spaced point potentials

We describe a non-perturbative method for computing the energy band structures of one-dimensional models with general point potentials sitting at equally spaced sites. This is done thanks to a Bethe ansatz approach and the method is applicable even when periodicity is broken, that is when Bloch's theorem is not valid any more. We derive the general equation governing the energy spectrum and illustrate its use in various situations. In particular, we get exact results for boundary effects. We also study non-perturbatively the effects of impurities in such systems. Finally, we discuss the possibility of including interactions between the particles of these systems.     

Quantum Phase Transitions in Matrix Product States

We present a new general and much simpler scheme to construct various quantum phase transitions （Q, PTs） in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state （MPS） OPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of Q, PT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous.     

Gibbs-Non-Gibbs Transitions via Large Deviations: Computable Examples

We give new and explicitly computable examples of Gibbs-non-Gibbs transitions of mean-field type, using the large deviation approach introduced in (van Enter et al. in Mosc. Math. J. 10:687–711, 2010). These examples include Brownian motion with small variance and related diffusion processes, such as the Ornstein-Uhlenbeck process, as well as birth and death processes. We show for a large class of initial measures and diffusive dynamics both short-time conservation of Gibbsianness and dynamical Gibbs-non-Gibbs transitions.     

Statistical Physics Of Opinion Formation: Is it a SPOOF?

We present a short review based on the nonlinear q-voter model about problems and methods raised within statistical physics of opinion formation (SPOOF). We describe relations between models of opinion formation, developed by physicists, and theoretical models of social response, known in social psychology. We draw attention to issues that are interesting for social psychologists and physicists. We show examples of studies directly inspired by social psychology like: “independence vs. anticonformity” or “personality vs. situation”. We summarize the results that have been already obtained and point out what else can be done, also with respect to other models in SPOOF. Finally, we demonstrate several analytical methods useful in SPOOF, such as the concept of effective force and potential, Landau's approach to phase transitions, or mean-field and pair approximations.     

Quantum Phase Transitions in Conventional Matrix Product Systems

For matrix product states(MPSs) of one-dimensional spin-\(\frac {1}{2}\) chains, we investigate a new kind of conventional quantum phase transition(QPT). We find that the system has two different ferromagnetic phases; on the line of the two ferromagnetic phases coexisting equally, the system in the thermodynamic limit is in an isolated mediate-coupling state described by a paramagnetic state and is in the same state as the renormalization group fixed point state, the expectation values of the physical quantities are discontinuous, and any two spin blocks of the system have the same geometry quantum discord(GQD) within the range of open interval (0,0.25) and the same classical correlation(CC) within the range of open interval (0,0.75) compared to any phase having no any kind of correlation. We not only realize the control of QPTs but also realize the control of quantum correlation of quantum many-body systems on the critical line by adjusting the environment parameters, which may have potential application in quantum information fields and is helpful to comprehensively and deeply understand the quantum correlation, and the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems.     

Gravity as a Source of Phase Transitions

After going through several distinguished examples, we argue that gravity is definitely a source of phase transitions of quite different nature: usual scalar effective potential ones, chiral symmetry transitions and even transitions involving the chromomagnetic vacuum. In such context, we emphasize the fact that curvature-induced phase transitions of those kinds—where an interplay between general relativity and elementary particle physics occurs—can be used in the construction of new models of the inflationary universe.     

Absence of second-order phase transitions in the Dobrushin uniqueness region

The Dobrushin uniqueness theorem assures that in a very large class of high-temperature classical statistical mechanical lattice models with short or long range, many-body interactions, and arbitrary compact spin space there are no first-order phase transitions. It will be shown that for the same class of interactions there are also no second-order phase transitions.Research partially supported by the National Science Foundation under Grant MCS 78-00688.     

Metric-Space Approach for Distinguishing Quantum Phase Transitions in Spin-Imbalanced Systems

Metric spaces are characterized by distances between pairs of elements. Systems that are physically similar are expected to present smaller distances (between their densities, wave functions, and potentials) than systems that present different physical behaviors. For this reason, metric spaces are good candidates for probing quantum phase transitions, since they could identify regimes of distinct phases. Here, we apply metric space analysis to explore the transitions between the several phases in spin-imbalanced systems. In particular, we investigate the so-called FFLO (Fulde-Ferrel-Larkin-Ovchinnikov) phase, which is an intriguing phenomenon in which superconductivity and magnetism coexist in the same material. This is expected to appear for example in attractive fermionic systems with spin-imbalanced populations, due to the internal polarization produced by the imbalance. The transition between FFLO phase (superconducting phase) and the normal phase (non-superconducting) and their boundaries have been subject of discussion in recent years. We consider the Hubbard model in the attractive regime for which density matrix renormalization group calculations allow us to obtain the exact density function of the system. We then analyze the exact density distances as a function of the polarization. We find that our distances display signatures of the distinct quantum phases in spin-imbalanced fermionic systems: with respect to a central reference polarization, systems without FFLO present a very symmetric behavior, while systems with phase transitions are asymmetric.     

Pairwise Entanglement and Quantum Phase Transitions in Spin Systems

We examine several well-known quantum spin models and categorize the behaviour of pairwise entanglement at quantum phase transitions. A unitied picture on the connection between the entanglement and quantum phase transition in spin systems is presented.     

Phase transitions in small systems: Microcanonical vs. canonical ensembles

We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and interacting via Lennard-Jones-type pair potentials. By means of these simple examples it can be shown already that the microcanonical thermodynamic functions of a small system may exhibit rich oscillatory behavior and, in particular, singularities (non-analyticities) separating different microscopic phases. These microscopic phases may be identified as different microphysical dissociation states of the small system. The microscopic oscillations of microcanonical thermodynamic quantities (e.g., temperature, heat capacity, or pressure) should in principle be observable in suitably designed evaporation/dissociation experiments (which must realize the physical preconditions of the microcanonical ensemble). By contrast, singular phase transitions cannot occur, if a small system is embedded into an infinite heat bath (thermostat), corresponding to the canonical ensemble. For the simple model systems under consideration, it is nevertheless possible to identify a smooth canonical phase transition by studying the distribution of complex zeros of the canonical partition function.     

Yang-Lee theory for a nonequilibrium phase transition

To analyze phase transitions in a nonequilibrium system, we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish two regions of analyticity, which can be identified with two different phases. In a region of the parameter space, both of these phases coexist. The condensation point can be computed with high accuracy.     

An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.