Critical Point Of Phase Transition Research Articles

About the Coulomb phase transition

The possibility of detecting a gas-liquid Coulomb phase transition in nondegenerate nonideal two-component low-temperature plasma is discussed using the results of calculating parameters of the critical point and binodal of the gas-liquid phase transition by the Monte Carlo method in the basic pseudopotential low-temperature plasma “shelf coulomb” model. Based on these results, a range of values of thermodynamic functions is found in which the Coulomb phase transition can be observed. It is shown that this range of parameters is beyond the domain of existence of strongly ionized nondegenerate low-temperature two-component plasma.

Generalized Ehrenfest's equations and phase transition in black holes

In this paper, we generalize Ehrenfest's equations to systems having two work terms, i.e. systems with three degrees of freedom. For black holes with two work terms we obtain nine equations instead of two to be satisfied at the critical point of a second-order phase transition. We finally generalize this method to a system with an arbitrary number of degrees of freedom and found there is [Formula: see text] equations to be satisfied at the point of a second-order phase transition where N is number of work terms in the first law of thermodynamics.

Quantum phase transition by employing trace distance along with the density matrix renormalization group

We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs.

Different critical points of chiral and deconfinement phase transitions in (2 + 1)-dimensional fermion–gauge interacting model

Based on the truncated Dyson-Schwinger equations for fermion and massive boson propagators in QED(3), the fermion chiral condensate and the mass singularities of the fermion propagator via the Schwinger function are investigated. It is shown that the critical point of the chiral phase transition is apparently different from that of the deconfinement phase transition and in Nambu phase the fermion is confined only for small gauge-boson mass.

Sound Velocities for Dissolving AgI + LiCl Melts

The ultrasonic velocities of a molten stratified mixture at a molar ratio of 0.3AgI and 0.7LiCl (the composition corresponding to the top of the miscibility gap) were measured along the saturation line over a wide temperature range using the pulse method to establish the characteristics of mixing salts comprising different chemical bonds. It is shown that the coefficients of the temperature dependences for the sound velocities in the coexisting phases have opposite signs as a result of the superposition of the temperature and concentration factors. It is found that the difference, Δu, between the magnitudes of the sound velocities for the coexisting phases decreases with increasing temperature and becomes zero at 1250 K. This temperature corresponds to the critical phase transition point, Tc. The temperature dependence of the sound velocity difference, Δu, for the system studied is described by the equation Δu ≈ (Tc – T)β, where β = 0.900, which is close to the value 0.896 obtained for the previously investigated AgI+NaCl melt but is less than the value found for alkali halide melts (β = 1.02), in which long-range Coulomb forces between ions prevail. The results are discussed in terms of the peculiarity of the chemical bond in silver iodide.

Finite-size behavior near the critical point of QCD phase-transition

It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling form of the critical related observable is suggested. Its fixed point behavior at critical incident energy can be served as a reliable identification of a critical point and nearby boundary of QCD phase transition. How to experimentally find the fixed point behavior is demonstrated by using 3D-Ising model as an example. The validity of the method at finite detector acceptances at RHIC is also discussed.

Decay of graviton condensates and their generalizations in arbitrary dimensions

Classicalons are self-bound classical field configurations, which include black holes in general relativity. In quantum theory, they are described by condensates of many soft quanta. In this work, their decay properties are studied in arbitrary dimensions. It is found that generically the decays of other classicalons are enhanced compared to pure graviton condensates, i.e. black holes. The evaporation of higher dimensional graviton condensates turns out to match Hawking radiation solely due to nonlinearites captured by the classicalon picture. Although less stable than black holes, all self-bound condensates are shown to be stable in the limit of large mass. Like for black holes, the effective coupling always scales as the inverse of the number of constituents, indicating that these systems are at critical points of quantum phase transitions. Consequences for cosmology, astro-and collider physics are briefly discussed.

Observing a quantum phase transition by measuring a single spin

We show that the ground-state quantum correlations of an Ising model can be detected by monitoring the time evolution of a single spin alone, and that the critical point of a quantum phase transition is detected through a maximum of a suitably defined observable. A proposed implementation with trapped ions realizes an experimental probe of quantum phase transitions which is based on quantum correlations and scalable for large system sizes.

A quantum critical point from flavours on a compact space

We analyse a $2+1$ dimensional defect field theory on a two sphere in an external magnetic field. The theory is holographically dual to probe D5-branes in global AdS$_5\times S^5$ background. At any finite magnetic field only the confined phase of the theory is realised. There is a first order quantum phase transition, within the confined phase of theory, ending on a quantum critical point of a second order phase transition. We analyse the condensate and magnetisation of theory and construct its phase diagram. We study the critical exponents near the quantum critical point and find that the second derivatives of the free energy, with respect to the bare mass and the magnetic field, diverge with a critical exponent of $-2/3$. Next, we analyse the meson spectrum of the theory and identify a massless mode at the critical point signalling a diverging correlation length of the quantum fluctuations. We find that the derivative of the meson mass with respect to the bare mass also diverges with a critical exponent of $-2/3$. Finally, our studies of the magnetisation uncover a persistent diamagnetic response similar to that in mesoscopic systems, such as quantum dots and nano tubes.

Critical point of gas-liquid type phase transition and phase equilibrium functions in developed two-component plasma model.

A two-component plasma model, which we called a "shelf Coulomb" model has been developed in this work. A Monte Carlo study has been undertaken to calculate equations of state, pair distribution functions, internal energies, and other thermodynamics properties. A canonical NVT ensemble with periodic boundary conditions was used. The motivation behind the model is also discussed in this work. The "shelf Coulomb" model can be compared to classical two-component (electron-proton) model where charges with zero size interact via a classical Coulomb law. With important difference for interaction of opposite charges: electrons and protons interact via the Coulomb law for large distances between particles, while interaction potential is cut off on small distances. The cut off distance is defined by an arbitrary ɛ parameter, which depends on system temperature. All the thermodynamics properties of the model depend on dimensionless parameters ɛ and γ = βe(2)n(1/3) (where β = 1/kBT, n is the particle's density, kB is the Boltzmann constant, and T is the temperature) only. In addition, it has been shown that the virial theorem works in this model. All the calculations were carried over a wide range of dimensionless ɛ and γ parameters in order to find the phase transition region, critical point, spinodal, and binodal lines of a model system. The system is observed to undergo a first order gas-liquid type phase transition with the critical point being in the vicinity of ɛ(crit) ≈ 13(T(*)(crit) ≈ 0.076), γ(crit) ≈ 1.8(v(*)(crit) ≈ 0.17), P(*)(crit) ≈ 0.39, where specific volume v* = 1/γ(3) and reduced temperature T(*) = ɛ(-1).

Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations

We theoretically study topological phase transitions in four generalized versions of the Kane-Mele-Hubbard model with up to $2\ifmmode\times\else\texttimes\fi{}{18}^{2}$ sites. All models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo (QMC) calculations to be performed to extremely low temperatures. We numerically compute the ${\mathbb{Z}}_{2}$ invariant and spin Chern number ${C}_{\ensuremath{\sigma}}$ directly from the zero-frequency single-particle Green's functions, and study the topological phase transitions driven by the tight-binding parameters at different on-site interaction strengths. The ${\mathbb{Z}}_{2}$ invariant and spin Chern number, which are complementary to each another, characterize the topological phases and identify the critical points of topological phase transitions. Although the numerically determined phase boundaries are nearly identical for different system sizes, we find strong system-size dependence of the spin Chern number, where quantized values are only expected upon approaching the thermodynamic limit. For the Hubbard models we considered, the QMC results show that correlation effects lead to shifts in the phase boundaries relative to those in the noninteracting limit, without any spontaneously symmetry breaking. The interaction-induced shift is nonperturbative in the interactions and cannot be captured within a ``simple'' self-consistent calculation either, such as Hartree-Fock. Furthermore, our QMC calculations suggest that quantum fluctuations from interactions stabilize topological phases in systems where the one-body terms preserve the ${D}_{3}$ symmetry of the lattice, and destabilize topological phases when the one-body terms break the ${D}_{3}$ symmetry.

Robust thermal quantum correlation and quantum phase transition of spin system on fractal lattices

We investigate the quantum correlation measured by quantum discord (QD) for thermalized ferromagnetic Heisenberg spin systems in one-dimensional chains and on fractal lattices using the decimation renormalization group approach. It is found that the QD between two non-nearest-neighbor end spins exhibits some interesting behaviors which depend on the anisotropic parameter Δ, the temperature T, and the size of system L. With increasing Δ continuously, the QD possesses a cuspate change at Δ = 0 which is a critical point of quantum phase transition (QPT). There presents the “regrowth” tendency of QD with increasing T at Δ 0. As the size of the system L becomes large, there still exists considerable thermal QD between long-distance end sites in spin chains and on the fractal lattices even at unentangled states, and the long-distance QD can spotlight the presence of QPT. The robustness of QD on the diamond-type hierarchical lattices is stronger than that in spin chains and Koch curves, which indicates that the fractal can affect the behaviors of quantum correlation.

Nonlinear response for external field and perturbation in the Vlasov system.

A nonlinear response theory is provided by use of the transient linearization method in the spatially one-dimensional Vlasov systems. The theory inclusively gives responses to external fields and to perturbations for initial stationary states, and is applicable even to the critical point of a second-order phase transition. We apply the theory to the Hamiltonian mean-field model, a toy model of a ferromagnetic body, and investigate the critical exponent associated with the response to the external field at the critical point in particular. The obtained critical exponent is the nonclassical value 3/2, while the classical value is 3. However, interestingly, one scaling relation holds with another nonclassical critical exponent of susceptibility in the isolated Vlasov systems. Validity of the theory is numerically confirmed by directly simulating temporal evolutions of the Vlasov equation.

Analysis of ionic fragment size distribution in collision of nanosecond laser with the C60 molecule

At the critical point of fragmentation phase transition occurring in C60 system, we found that the yield distribution of ionic fragments Cn+ (n=3-16) originating from the multi-fragmentation pattern can be approximated fairly well by a power-law attenuation form of n−λ. Under the framework of Fisher model, the experimental result implies that the ionization-degree distribution of fragments obeys a power law enhancement form as the size n.

Measurement of Critical correlations in an ultracold Bose gas by means of a temporal Talbot-Lau interferometery

We report the results of a study of measuring the correlation length at the Lambda critical phase transition point in an ultra-cold Bose gas with a temporal Talbot-Lau (TL) interferometery. Near the critical temperature, the correlation length increase exponentially and its critical exponent factor is measured around 0.67, which is a universal value in quantum gas. In the experiment we filtered the fraction of condensate from the thermal cloud at the Lambda critical phase transition point by means of the TL interferometer technique.

Quantum phase transition in the U(2) vibron model and the critical point symmetry

The quantum phase transition in the U(2) vibron model is investigated in large- N limit with the coherent state method and for finite N in a numerical scheme Through analyzing the potential structure and the corresponding low-lying spectrum, it is found that the dynamical characters at the critical point can be approximately described by the E (1) critical point symmetry, but such an approximation becomes poor with the increasing of the excitation energy. In addition, the scaling behavior of the spectrum at the critical point has been also investigated in a numerical way. The results indicate that the scaling law of the spectrum at the critical point of the 2nd order phase transition may be independent of the dimension of system.

Black holes as critical point of quantum phase transition.

We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose–Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs.

Energy and centrality dependence of dynamical higher cumulant of proton multiplicity distributions at RHIC

Higher cumulant of baryon number is suggested to be a good probe of critical point of QCD phase transition in relativistic heavy ion collisions. The energy and centrality dependence of dynamical kurtosis for Au + Au collisions at RHIC beam energies [Formula: see text] are measured. The dynamical kurtosis of both net and total protons are studied and their sign behaviors are discussed. The results are compared with those from transport model of AMPT. The contribution of non-critical effect on centrality definition is investigated.

Symmetry-based approach to ground-state properties of the one-dimensional negative-U Bose–Hubbard trimer model

It is shown that the ground state of the one-dimensional negative-U three-site Bose–Hubbard (trimer) model with periodic (boundary) condition or for a closed chain can be solved almost exactly within a small symmetric subspace with a few boson-trines through an analysis of the percentage of the boson-trines in the ground state. It is also shown that there is a sudden increase of the boson-trine content of the ground state near the critical point of the quantum phase transition, which may be used as an effective order parameter to study the phase transition of the model. The ground-state energy per particle and the entanglement measure with the variation of the control parameter are also analyzed to show their transitional behavior.

Scrambling in the black hole portrait

Recently a quantum portrait of black holes was suggested according to which a macroscopic black hole is a Bose-Einstein condensate of soft gravitons stuck at the critical point of a quantum phase transition. We explain why quantum criticality and instability are the key for efficient generation of entanglement and consequently of the scrambling of information. By studying a simple Bose-Einstein prototype, we show that the scrambling time, which is set by the quantum break time of the system, goes as $\log N \,$ for $N$ the number of quantum constituents or equivalently the black hole entropy.