Critical Point In Terms Research Articles

Emergent topological excitations in a two-dimensional quantum spin system

We study the mechanism of decay of a topological (winding-number) excitation due to finite-size effects in a two-dimensional valence-bond solid state, realized in an $S=1/2$ spin model ($J$-$Q$ model) and studied using projector Monte Carlo simulations in the valence bond basis. A topological excitation with winding number $|W|>0$ contains domain walls, which are unstable due to the emergence of long valence bonds in the wave function, unlike in effective descriptions with the quantum dimer model. We find that the life time of the winding number in imaginary time diverges as a power of the system length $L$. The energy can be computed within this time (i.e., it converges toward a "quasi-eigenvalue" before the winding number decays) and agrees for large $L$ with the domain-wall energy computed in an open lattice with boundary modifications enforcing a domain wall. Constructing a simplified two-state model and using the imaginary-time behavior from the simulations as input, we find that the real-time decay rate out of the initial winding sector is exponentially small in $L$. Thus, the winding number rapidly becomes a well-defined conserved quantum number for large systems, supporting the conclusions reached by computing the energy quasi-eigenvalues. Including Heisenberg exchange interactions which brings the system to a quantum-critical point separating the valence-bond solid from an antiferromagnetic ground state (the putative "deconfined" quantum-critical point), we can also converge the domain wall energy here and find that it decays as a power-law of the system size. Thus, the winding number is an emergent quantum number also at the critical point, with all winding number sectors becoming degenerate in the thermodynamic limit. This supports the description of the critical point in terms of a U(1) gauge-field theory.

Ring-exchange periodic Anderson model for3Hebilayers

We present numerical results of a model calculation for the 3He bilayer system, which captures the interplay between fast and slow dynamics of the different layers and incorporates an independent scale for the three body ring exchange. By means of Cluster-DMFT+CTQMC, we find remarkable similarities with the experiments: a suppression of the coherence temperature upon approaching the solidification point of the first layer accompanied by the onset of strong ferromagnetic correlations within the first layer. Based on the consistent results for different cluster sizes we conjecture a first-order transition cutting short the Kondo breakdown, which allows us to interpret the experimental observation of an intervening phase preempting the quantum critical point in terms of a phase separation.

Effect of an external magnetic field on a critical point for phase separation in a dusty plasma

The effect of an external magnetic field on a critical point for phase transitions in a dusty plasma is investigated. It is shown that the ambient magnetic field increases the effective hard core radius of dust particles, which, in turn, would affect a critical point in terms of the Coulomb coupling parameter and the ratio between the inter-dust grain spacing and the dusty plasma Debye radius. The present result may be useful in understanding the phenomenon of liquid–vapor phase transitions in laboratory dusty plasmas that are held in an external magnetic field.

Quantum structural phase transition in chains of interacting atoms

A quasi one--dimensional system of trapped, repulsively interacting atoms (e.g., an ion chain) exhibits a structural phase transition from a linear chain to a zigzag structure, tuned by reducing the transverse trap potential or increasing the particle density. Since it is a one dimensional transition, it takes place at zero temperature and therefore quantum fluctuations dominate. In [Fishman, et al., Phys. Rev. B 77, 064111 (2008)] it was shown that the system close to the linear-zigzag instability is described by a $\phi^4$ model. We propose a mapping of the $\phi^4$ field theory to the well known Ising chain in a transverse field, which exhibits a quantum critical point. Based on this mapping, we estimate the quantum critical point in terms of the system parameters. This estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs, and which has a finite, measurable deviation from the critical point evaluated within the classical theory. A measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures T. We focus in particular on a trapped ion system, and estimate the implied limitations on T and on the interparticle distance. We conclude that the experimental observation of the quantum critical behavior is in principle accessible.

Quantum Zigzag Transition in Ion Chains

A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one-dimensional optical lattice.

“Squishy capacitor” model for electrical double layers and the stability of charged interfaces

Negative capacitance (NC), predicted by various electrical double layer (EDL) theories, is critically reviewed. Physically possible for individual components of the EDL, the compact or diffuse layer, it is strictly prohibited for the whole EDL or for an electrochemical cell with two electrodes. However, NC is allowed for the artificial conditions of sigma control, where an EDL is described by the equilibrium electric response of electrolyte to a field of fixed, and typically uniform, surface charge-density distributions, sigma. The contradiction is only apparent; in fact local sigma cannot be set independently, but is established by the equilibrium response to physically controllable variables, i.e., applied voltage phi (phi control) or total surface charge q (q control). NC predictions in studies based on sigma control signify potential instabilities and phase transitions for physically realizable conditions. Building on our previous study of phi control [M. B. Partenskii and P. C. Jordan, Phys. Rev. E 77, 061117 (2008)], here we analyze critical behavior under q control, clarifying the basic picture using an exactly solvable "squishy capacitor" toy model. We find that phi can change discontinuously in the presence of a lateral transition, specify stability conditions for an electrochemical cell, analyze the origin of the EDL's critical point in terms of compact and diffuse serial contributions, and discuss perspectives and challenges for theoretical studies not limited by sigma control.

The statistical mechanics of vesicles

Partially convex polygons, Exact solution, q-series asymptotics, Scaling function. I discuss two-dimensional lattice models of closed fluctuating membranes, or vesicles (11. The underlying mathematical model is that of self-avoiding polygons and their enumeration by perime- ter and area.. Physically, this model is of interest as its phase diagram contains a point at which tricritical scaling is observed [2]. By adding the constraint of partial directedness, one gets combinatorial models related to the partitioning of integers. These models are solvable in the sense that an explicit expression for the generating function can be given [3,4]. The derivation of this generating function involves a nonlinear functional equation, and the solution is given in terms of alternating q-series. The asymptotic analysis of these generating functions can be done with the help of a new contour integral representation. This leads to an explicit calculation of the scaling behaviour around the critical point in terms of the Airy function [5]. In particular, one gets a uniform asymptotic expansion of the involved q-series as

Length scales and power laws in the two-dimensional forest-fire model

We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees. We check resp. improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode. We also investigate the possibility of describing the critical point in terms of a distribution of the global density. We find that some qualitative features such as a temporal oscillation and a power law of the cluster-size distribution can nicely be obtained from such a model that discards the spatial structure.

Theory of binary mixtures of a flexible polymer and a liquid crystal

A simple model is presented to describe the phase behavior in binary mixtures of a flexible polymer and a liquid crystal. By using the incompressible approximation to the Onsager theory which combined both the excluded volume interactions between the liquid crystals and the attractive interaction due to the alignment of the liquid crystals, we obtain the free energy of mixing of the binary mixtures. The derived free energy consists of two terms: the free energy of mixing of Flory–Huggins type for polymer blends and the free energy change due to the alignment of the liquid crystals. We predict the nematic–isotropic phase separation and the isotropic–isotropic one with a critical point in terms of the Flory–Huggins and Maier–Saupe interaction parameters. The results are compared with the observed phase diagrams. We also discuss the phase separation in solutions of rigid-rodlike molecules.

Low-dose dopamine hastens onset of gut ischemia in a porcine model of hemorrhagic shock.

Gut metabolism may become anaerobic before the whole body during progressive phlebotomy in dogs. Because dopamine has selective mesenteric vasodilator effects, we asked whether dopamine could delay onset of bowel ischemia during hemorrhagic shock. We studied whole body and gut O2 consumption (VO2) and O2 delivery (QO2) using progressive phlebotomy in anesthetized pigs. Nine pigs received a dopamine infusion of 2 micrograms.kg-1.min-1, whereas a control group of seven pigs received equivalent saline infusion. Onset of ischemia in whole body and gut was determined as critical O2 delivery (QO2c), the intersection point of biphasic regression on plots of VO2-QO2 relationships. Blood flow and O2 extraction were measured as mechanisms of gut ischemia for entire in situ small and large gut using a superior mesenteric venous fistula. Dopamine hastened onset of gut ischemia relative to onset of whole body ischemia (gut critical point in terms of whole body QO2 9.9 +/- 2.1 ml O2.kg-1.min-1, whole body QO2c 7.8 +/- 0.7 ml O2.kg-1.min-1, P less than 0.01). In contrast, onset of gut ischemia in control animals occurred at same time as onset of whole body ischemia (gut critical point in terms of whole body QO2 7.4 +/- 2.3 ml O2.kg-1.min-1, whole body QO2c 7.1 +/- 2.7 ml O2.kg-1.min-1, P = not significant). Hastening of onset of gut ischemia in dopamine-treated animals was associated with decreased ability of gut to extract O2. Low-dose dopamine was not protective against gut ischemia during shock but rather caused earlier onset of gut ischemia during hemorrhagic shock.

Order parameter and a critical point on the megabar-pressure hydrogen-A phase line.

We present experimental evidence that a critical point, also reported by Hemley and Mao, exists for the hydrogen-A phase line at a pressure of 173(4) GPa and 151(15) K. We give an interpretation of this critical point in terms of its relationship to a low-pressure disordered insulating phase and a possible metallic phase at high pressure. We interpret the temeprature dependence of the vibron frequency of the H-A phase as a measure of one of the two order parameters characterizing this phase.

Fluctuating pseudoatoms in metallic fluids

The nature of long-range many-body interactions in metallic fluids is examined with emphasis on their possible role in the unique features of these systems observed near the liquid–vapor critical point. A reexamination of recent theoretical results demonstrating the existence of van der Waals forces between ‘‘pseudoatoms’’ (ion cores and associated screening electrons) reveals a direct correspondence with dispersion forces in insulating systems. In the limit of high conduction electron number densities ρ, pseudoatoms have an effective frequency-dependent polarizability α(ω)=α(0)ω2p/(ω2p−ω2), where α(0)=z/4πρ, with z the ion valence, and ωp is the classical electron gas plasma frequency (4πρe2/m)1/2. It is the dynamic nature of the interactions (arising from fluctuations of the pseudoatoms) that permits such a long-range interaction to exist. The dimensionless parameter α(0)ρ which in insulating fluids characterizes the relative importance of triplet (Axilrod–Teller) to pair dispersion interactions is thus system independent and significantly larger than in nonmetallic fluids. The nature of this dynamic polarizability is further examined in the context of a transport theory for a classical plasma based on the Boltzmann equation. The statistical mechanics of fluctuating pseudoatoms at finite temperature is studied both for the metallic fluid and in the Wigner crystal. These various approaches suggest that the pseudoatom interaction may be viewed as a potential mediated by the exchange of plasmons, just as conventional van der Waals forces arise from the exchange of virtual excitations of atomic levels. A description of the critical point in terms of pseudoatom interactions appears to explain qualitatively the extreme liquid–vapor asymmetry of the coexistence curves of cesium and rubidium as arising from the magnitude of three-body interactions. Additionally, it suggests that the thermal energy at the critical point scales with the plasmon energy, consistent with experiment.

Possible Charged Pion Condensation in Neutron Matter with Small Proton Admixture

Since Migdal!) and Sawyer-Scalapino ) pointed out the possibility of pion condensation in nuclear matter, it has intensively studied not only on the pionic instability but also on the structure of pion condensed state. ) Possible spin, isospin and space structures of pion condensate were also considered in detail in both pure neutron matter and isosymmetric nuclear matter. 3 ).4) In a realistic neutron star. there exists an admixture of protons, equilibrating with electrons. These protons give rise to the characteristic pion condensate, so-called Jr, +-condensate, above some critical density. Its possibility has originally been suggested by Migdal, Markin and Mishustin in pure neutron matter though much qualitative as follows: even in pure neutron matter (Z = 0) there exists the energy branch of sound (w~+)<o) with the same quantum number as the positive pion. Iw~+)1 increases as the nucleon density P (=Pn, the neutron density in the case) to lead to overcome the neutron Fermi energy, that is w~+) +EW)=O. Then there occurs the instability of Jr, + in a sense of the Landau 2nd order phase transition. More rigorous statements will be done later. The critical density is estimated as Pc(Jr,+)/Po~O.4, where po is the normal density (Po' 0.5*»). The purpose of this paper is to study the Jr, +-condensate in a realistic iso-asymmetric nuclear matter (N;p.Z*O). In the case, the *) We take the natural unit as h= c= m~=l. critical density of this mode is considered to be the lowest as compared with the other kind of pion condensates. *) The energy gain of the system, the structure of the nucleon system and the relation with the so-called Jr±pair condensation leading from the instability of spontaneous production of Jr, +-sound excitation and Jr--pion one are the main subjects. On the transition mechanism from Jr, +-condensate to Jr±-pair one, it has been pointed oue) that the instability corresponding to Jr±-pair condensation does not arise, if the existence of Jr. +-condensate is taken into account. And the transition from Jr, +-condens ate to Jr±-pair one was suggested ) in the system with Z*O. On this subject we consider in detail. In order to get the qualitative understandings, we take only p-wave Jr-N interaction. First, we consider the behavior of the total energy of the system near the critical point in terms of the Landau formalism. The effective Hamiltonian is given as

Nonfood uses of plants in Usambara

The attempt here has been to discuss Shambaa use of wild nonfood plants primarily in terms of utility, but also with some attention to principles of classification and of the effects of human use of plants on the wider environment. The local system of classification emphasizes those plants which are useful to people. There are many of these, which may be surprising in an area that has been undergoing commercialization and socio-economic change since the early years of this century (P. Fleuret, 1979). Natural systems still provide the Shambaa with many useful, even essential products. But those plants that are useful are also being used up, and continued exploitation has ramifications for the other components of the ecosystem: fish vanished from the streams, wild date palms and tree ferns vanishing, deforestation, erosion, fuelwood shortages, increasing prices for many natural products. By all indications, the most crucial effects of human exploitation have occurred within the last 100 years. Contemporary accounts by missionaries and explorers describe the area as “... abound[ing] in forests of fine timber ...” (Krapf, 1860) or cite oral traditions indicating that the most seriously deforested areas of today were under forest just prior to the turn of the century. (Data obtained from Lushoto District files lodged at the Tanzania National Archives, Dar es Salaam.) As recently as 1975, one author, in writing of Usambara, suggested that a solution to agricultural crisis (especially land shortage) was to open the remaining forest reserve to human settlement and cultivation (Cliffe, 1975, pp. 149–150). This suggestion does not take into account the fact that the natural vegetation of Usambara continues to provide its residents with a great many vital materials and implements, even though human use of these resources is approaching, or has even reached, a critical point in terms of ecological consequences. Efforts should be made to preseve, not destroy, this vital natural resource.