Critical Point Of Phase Transition Research Articles

Critical behavior of 3D [formula omitted] lattice gauge theories at zero temperature

Three-dimensional Z(N) lattice gauge theories at zero temperature are studied for various values of N. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized Z(N) model for N=2,3,4,5,6,8. Numerical computations are used to simulate vector models for N=2,3,4,5,6,8,13,20 for lattices with linear extension up to L=96. We locate the critical points of phase transitions and establish their scaling with N. The values of the critical indices indicate that the models with N>4 belong to the universality class of the three-dimensional XY model. However, the exponent α derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle.

Correlation dynamics of a qubit—qutrit system in a spin-chain environment with Dzyaloshinsky—Moriya interaction

We study the dynamics of correlations for a hybrid qubit—qutrit system in an XY spin-chain environment with Dzyaloshinsky—Moriya interaction. Our discussion involves a comparative analysis of negativity, quantum discord, and measurement-induced disturbance. It is found that the quantum discord is optimal of the three quantum correlations to detect the critical point of quantum phase transition. Only when the qubit interacts with the environment, is the phenomenon of sudden transition between the classical correlation and the quantum discord observed. Moreover, the Dzyaloshinsky—Moriya interaction enhances the decay of quantum correlations.

Signatures of electronic phase separation in the Hall effect of anisotropically strained La0.67Ca0.33MnO3 films

Systematic transport measurements have been performed on a series of La0.67Ca0.33MnO3 thin films with varying degrees of anisotropic strain. The strain is induced via epitaxial growth on NdGaO3(001) substrates and varied by controlling the thermal annealing time. An antiferromagnetic insulating (AFI) state, possibly associated with charge ordering, emerges upon thermal annealing. The Hall effect in these materials exhibits features that are indicative of a percolative phase transition and correlate closely with the emergence of the AFI state. In the paramagnetic phase, the Hall resistivity takes on two slopes in all samples: a decreasing negative slope with increasing temperature at low fields, which is attributed to the carrier hopping motion, and an almost temperature independent positive slope at high fields due to diffusive transport of holes. Significantly, the crossover fields of the Hall resistivity slope at different temperatures correspond to the same magnetization, which is interpreted as the critical point of a magnetic field-driven percolative phase transition. At lower temperatures near the zero-field metal–insulator transition, pronounced enhancement of the Hall coefficient with the development of the AFI state is observed. The enhancement peaks near the magnetic field-driven percolation; its magnitude correlates with the strength of the AFI state and is suppressed with the melting of the AFI state by an in-plane magnetic field. The observations resemble many features of the enhancement of the Hall coefficient in granular metal films near the composition-driven percolation.

Simultaneous quadrupole and octupole shape phase transitions in Thorium

The evolution of quadrupole and octupole shapes in Th isotopes is studied in the framework of nuclear Density Functional Theory. Constrained energy maps and observables calculated with microscopic collective Hamiltonians indicate the occurrence of a simultaneous quantum shape phase transition between spherical and quadrupole-deformed prolate shapes, and between non-octupole and octupole-deformed shapes, as functions of the neutron number. The nucleus 224Th is closest to the critical point of a double phase transition. A microscopic mechanism of this phenomenon is discussed in terms of the evolution of single-nucleon orbitals with deformation.

Efficient simulation of the random-cluster model

The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.

Phase diagram of a cyclic predator-prey model with neutral-pair exchange

In this paper we obtain the phase diagram of a four-species predator-prey lattice model by using the proposed gradient method. We consider cyclic transitions between consecutive states, representing invasion or predation, and allowed the exchange between neighboring neutral pairs. By applying a gradient in the invasion rate parameter one can see, in the same simulation, the presence of two symmetric absorbing phases, composed by neutral pairs, and an active phase that includes all four species. In this sense, the study of a single-valued interface and its fluctuations give the critical point of the irreversible phase transition and the corresponding universality classes. Also, the consideration of a multivalued interface and its fluctuations bring the percolation threshold. We show that the model presents two lines of irreversible first-order phase transition between the two absorbing phases and the active phase. Depending on the value of the system parameters, these lines can converge into a triple point, which is the beginning of a first-order irreversible line between the two absorbing phases, or end in two critical points belonging to the directed percolation universality class. Standard simulations for some characteristic values of the parameters confirm the order of the transitions as determined by the gradient method. Besides, below the triple point the model presents two standard percolation lines in the active phase and above a first-order percolation transition as already found in other similar models.

Quantum transition-edge detectors

Small perturbations to systems near critical points of quantum phase transitions can induce drastic changes in the system properties. Here I show that this sensitivity can be exploited for weak-signal detection applications. This is done by relating a widely studied signature of quantum chaos and quantum phase transitions known as the Loschmidt echo to the minimum error probability for a quantum detector and noting that the echo, and therefore the error, can be significantly reduced near a critical point. Three examples, namely, the quantum Ising model, the optical parametric oscillator model, and the Dicke model, are presented to illustrate the concept. For the latter two examples, the detectable perturbation can exhibit a Heisenberg scaling with respect to the number of detectors, even though the detectors are not entangled and no special quantum state preparation is specified.

Recurrence of spatio-temporal patterns of spikes and neural avalanches at the critical point of a non-equilibrium phase transition

Recently, many experimental results have supported the idea that the brain operates near a critical point [1-5], as reflected by the power laws of avalanche size distributions and maximization of fluctuations. Several models have been proposed as explanations for the power law distributions that emerge in spontaneous cortical activity [6,5]. Models based on branching processes and on self-organized criticality are the most relevant. However, there are additional features of neuronal avalanches that are not captured in these models, such as the stable recurrence of particular spatiotemporal patterns and the conditions under which these precise and diverse patterns can be retrieved [4]. Indeed, neuronal avalanches are highly repeatable and can be clustered into statistically significant families of activity patterns that satisfy several requirements of a memory substrate. In many areas of the brain having different brain functionality, repeatable precise spatiotemporal patterns of spikes seem to play a crucial role in the coding and storage of information. Many in vitro and in vivo studies have demonstrated that cortical spontaneous activity occurs in precise spatiotemporal patterns, which often reflect the activity produced by external or sensory inputs. The temporally structured replay of spatiotemporal patterns has been observed to occur, both in the cortex and hippocampus, during sleep and in the awake state, and it has been hypothesized that this replay may subserve memory consolidation. Previous studies have separately addressed the topics of phase-coded memory storage and neuronal avalanches, but our work is the first to show how these ideas converge in a single cortical model. We study a network of leaky integrate- and-fire (LIF) neurons, whose synaptic connections are designed with a rule based on spike-timing dependent plasticity (STDP). The network works as an associative memory of phase-coded spatiotemporal patterns, whose storage capacity has been studied in [7]. In this paper, we study the spontaneous dynamics when the excitability of the model is tuned to be at the critical point of a phase transition, between the successful persistent replay and non-replay of encoded patterns. We introduce an order parameter, which measures the overlap (similarity) between the activity of the network and the stored patterns. We find that, depending on the excitability of the network, different working regimes are possible. For high excitability, the dynamical attractors are stable, and a collective activity that replays one of the stored patterns emerges spontaneously, while for low excitability, no replay is induced. Between these two regimes, there is a critical region in which the dynamical attractors are unstable, and intermittent short replays are induced by noise. At the critical spiking threshold, the order parameter goes from zero to one, and its fluctuations are maximized, as expected for a phase transition (and as observed in recent experimental results in the brain [5]). Notably, in this critical region, the avalanche size and duration distributions follow power laws. Critical exponents are consistent with a scaling relationship observed recently in neural avalanches measurements. In conclusion, our simple model suggests that avalanche power laws in cortical spontaneous activity may be the effect of a network at the critical point between the replay and non-replay of spatiotemporal patterns. Interestingly in the cortex, the emergence of power law distributions of avalanche sizes depends on an optimal concentration of dopamine and on the balance of excitation and inhibition, suggesting that particular parameters must be appropriately tuned. This may suggest that the cortex operates near the critical point of a phase transition, characterized by a critical value of excitability.

Determination of the similarity criteria for thermal gravitational convection in a supercritical fluid

Natural-convection flows in continua are studied at the parameter values beyond the critical point of the liquid-gas phase transition. The theory of similarity of supercritical convective flows is generalized by taking account for the dependence of the thermodynamic properties of a medium on the temperature and the density. In the case of an arbitrary two-parameter medium calibration relations, which serve for determining the similarity criteria of convection, are derived. In the fluid with the Van der Waals equation of state the calibration relations are reduced to the form of functions of the dimensionless temperature and density.

Monte Carlo simulation of the nonadditive restricted primitive model of ionic fluids: Phase diagram and clustering

We report an accurate Monte Carlo calculation of the phase diagram and clustering properties of the restricted primitive model with nonadditive hard-sphere diameters. At high density the positively nonadditive fluid shows more clustering than in the additive model and the negatively nonadditive fluid shows less clustering than in the additive model; at low density the reverse scenario appears. A negative nonadditivity tends to favor the formation of neutrally charged clusters starting from the dipole. A positive nonadditivity favors the pairing of like ions at high density. The critical point of the gas-liquid phase transition moves at higher temperatures and higher densities for a negative nonadditivity and at lower temperatures and lower densities for a positive nonadditivity. The law of corresponding states does not seem to hold strictly. Our results can be used to interpret recent experimental works on room temperature ionic liquids.

Densities of a dissolving mixture of molten (AgI + NaCl)

The densities of a molten mixture of (0.5AgI+0.5NaCl) were measured along the saturation line over a wide temperature range by the hydrostatic weight method to establish the peculiarities of the mixing of salts with different chemical bonds. We showed that the difference between the magnitudes of the densities for the coexisting phases decreases with increasing temperature and becomes equal to zero at 1063.5K. This temperature corresponds to the critical phase transition point, Tc. The temperature dependence of the difference in densities, Δρ, is described by equation Δρ/ρc≈Tc-TTcβ, where ρc is the density at Tc. The index β=0.476 occurs at a lower value than that found for alkali halide melts (β=0.52) where long-range Coulombic forces between ions prevail.

Thermomechanical approach to modeling the loading diagram

A thermodynamic model of the loading diagram for the standard sample as an open system, which has critical points of second-order phase transitions with the formation of dissipative structures (by Prigozhin) and excludes the angular points, is suggested. The model is based on three postulates: the reversible nonlinear elastic deformation (by Cauchy), the parabolic mechanism of dislocation strengthening, and parabolic softening of the defects. The lifetime of the deformation of the sample (the material point) is determined as an integrated evaluation, which depends on coordinates and time. The model can be used to solve elastoplastic problems at small deformation and to evaluate the current lifetime.

The Earth as a living planet: human-type diseases in the earthquake preparation process

Abstract. The new field of complex systems supports the view that a number of systems arising from disciplines as diverse as physics, biology, engineering, and economics may have certain quantitative features that are intriguingly similar. The Earth is a living planet where many complex systems run perfectly without stopping at all. The earthquake generation is a fundamental sign that the Earth is a living planet. Recently, analyses have shown that human-brain-type disease appears during the earthquake generation process. Herein, we show that human-heart-type disease appears during the earthquake preparation of the earthquake process. The investigation is mainly attempted by means of critical phenomena, which have been proposed as the likely paradigm to explain the origins of both heart electric fluctuations and fracture-induced electromagnetic fluctuations. We show that a time window of the damage evolution within the heterogeneous Earth's crust and the healthy heart's electrical action present the characteristic features of the critical point of a thermal second-order phase transition. A dramatic breakdown of critical characteristics appears in the tail of the fracture process of heterogeneous system and the injured heart's electrical action. Analyses by means of Hurst exponent and wavelet decomposition further support the hypothesis that a dynamical analogy exists between the geological and biological systems under study.

Ultrasonic velocity for an equimolar mixture of molten AgI and NaCl in the biphasic region

The ultrasonic velocities of a molten stratifying mixture composed of 0.5 AgI and 0.5 NaCl (the composition corresponding to the top of the miscibility gap) were measured along the saturation line for a wide temperature range via the pulse method to establish the characteristics of mixing salts with different chemical bonds. We show that the difference, Δu, between the magnitudes of the sound velocities for the coexisting phases decreases with increasing temperature and becomes zero at 1064K. This temperature corresponds to the critical phase transition point, Tc. The temperature dependence of the sound velocity difference, Δu, is described by the equation Δu≈(Tc−T)Θ, where Θ=0.896, which is less than that found for alkali halide melts (Θ=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.

Trace distance and scaling behavior of a coupled cavity lattice at finite temperature

We use an alternative approach to study the quantum phase transition in a coupled cavity lattice at finite temperature. As an illustrative example, we investigate the behaviors of the trace distance and quantum phase transition in a Jaynes-Cummings lattice at finite temperature. It is found that the trace distance can be used to describe the critical point of the quantum phase transition at finite low temperatures and the critical points are sensitive to the atom-field interaction strength and the detuning factor. For non-equilibrium states, we demonstrate that the time evolution of the trace distance's maximum value is also a good indicator of the critical points. Moreover, we show that the scaling behavior of derivative of the trace distance at the critical points and the scaling rule are dependent on the external parameters of the Hamiltonian.

Exciton transfer dynamics in a trimer system

We study exciton transfer dynamics in a trimer system by investigating excitation transfer probability (ETP). We calculate ETP in the zero-temperature limit and theoretically predict the environment-assisted quantum critical effect, in which ETP exhibits a sudden change at the critical point of quantum phase transition for the trimer. In particular, we find that the steady-state ETP can be observed in the presence of the environment interaction.

Measurement-induced disturbance and thermal negativity in 1D optical lattice chain

We study the measurement-induced disturbance (MID) in a 1D optical lattice chain with nonlinear coupling. Special attention is paid to the difference between the thermal entanglement and MID when considering the influences of the linear coupling constant, nonlinear coupling constant and external magnetic field. It is shown that MID is more robust than thermal entanglement against temperature T and external magnetic field B, and MID may reveal more properties about quantum correlations of the system, which can be seen from the point of view that MID can be nonzero when there is no thermal entanglement and MID can detect the critical point of quantum phase transition at finite temperature.

New insights into quantum and classical correlations in XY spin models

We compute quantum dissonance Q (non-entangled quantum correlation), entanglement E, quantum discord D (total quantum correlation) and classical correlation C for spin pairs at any distance in the infinite XY spin-1/2 chains, i.e., the anisotropic XY model and the isotropic XY model with three-spin interactions. We obtain two simple dominance relations: C ≥ E and D ≥ E + Q Except this, there are no other simple ordering relations between them. We also show that Q can detect the special points of the system where the entanglement just appears or completely disappears. In addition, it is worthwhile to mention that dissonance and classical correlation can also clearly spotlight the critical points of quantum phase transitions in XY spin-1/2 chains.

Phase transition and scaling behavior of topological charged black holes in Hořava–Lifshitz gravity

Gravity can be thought as an emergent phenomenon and it has a nice ‘thermodynamic’ structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with the arbitrary scalar curvature 2k in Hořava–Lifshitz gravity at the Lifshitz point z = 3. The analysis is done using the canonical ensemble framework, i.e. the charge is kept fixed. We find (a) for both k = 0 and k = 1, there is no phase transition, (b) while k = −1 case exhibits the second-order phase transition within the physical region of the black hole. The critical point of second-order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamic scaling laws.

Strata formation at fast electrical explosion of cylindrical conductors

The process of electrical explosion of aluminum and tungsten wires at current densities above 108 A/cm2 (the fast electrical explosion regime) is investigated. Within the frame of 2D magnetohydrodynamic calculations based on the Particle-in-Cell technique with realistic equations of state of the metals, the processes of strata formation in the plasma are considered. In the fast electrical explosion regime, strata formation is shown to take place due to the overheat instability. The strata occurrence is caused by the character of the conductivity change near the critical point of the liquid-vapor phase transition, that is, by metal conductivity decrease with a temperature increase and a density decrease. To provoke strata formation, the energy deposited into the wire substance should be of about the sublimation energy.