Theory Of Continuous Phase Transitions Research Articles

Geometric properties of the complete-graph Ising model in the loop representation.

The exact solution of the Ising model on the complete graph (CG) provides an important, though mean-field, insight for the theory of continuous phase transitions. Besides the original spin, the Ising model can be formulated in the Fortuin-Kasteleyn random cluster and the loop representation, in which many geometric quantities have no correspondence in the spin representations. Using a lifted-worm irreversible algorithm, we study the CG-Ising model in the loop representation and, based on theoretical and numerical analyses, obtain a number of exact results including volume fractal dimensions and scaling forms. Moreover, by combining with the loop-cluster algorithm, we demonstrate how the loop representation can provide an intuitive understanding to the recently observed rich geometric phenomena in the random-cluster representation, including the emergence of two configuration sectors, two length scales, and two scaling windows.

Phase transition grade and microstructure of AdS black holes in massive gravity

Considering that under the framework of the massive gravity theory, the interaction between the mass gravitons and Schwarzschild black hole (BH) could make it carry a scalar charge, the phase transition process caused by this scalar charge is investigated in this analysis. The phase transition grade and microstructure of those BHs are investigated from both macroscopic and microscopic points of view. From the macroscopic point of view, it is found that Ehrenfest equations are satisfied at the phase transition critical point, which implies that the phase transition grade of those BHs is second-order. Based on the BH molecules model and Landau continuous phase transition theory, the phase transition of those BHs from the microcosmic point of view is analyzed. The critical exponents obtained from the two perspectives are consistent. By investigating the Ruppeiner geometry, the microstructure feature of those BHs is revealed. These results suggest that the phase transition of BH in massive gravity is a standard second-order phase transition at the critical point, and the microscopic details of those BHs are different from the Reissner–Nordström AdS BH in standard Einstein gravity.

Topological Frustration can modify the nature of a Quantum Phase Transition

Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. We show that topological frustration can change the nature of a second order quantum phase transition separating two different ordered phases. Even more remarkably, frustration is triggered simply by a suitable choice of boundary conditions in a 1D chain. While with every other BC each of two phases is characterized by its own local order parameter, with frustration no local order can survive. We construct string order parameters to distinguish the two phases, but, having proved that topological frustration is capable of altering the nature of a system's phase transition, our results pose a clear challenge to the current understanding of phase transitions in complex quantum systems.

Effect of Co and Mg doping at Cu site on structural, magnetic and dielectric properties of α–Cu2V2O7

We have studied the effect of doping of both magnetic (Co) and nonmagnetic (Mg) ions at the Cu site on phase transition in polycrystalline α–Cu2V2O7 through structural, magnetic, and electrical measurements. X-ray diffraction reveals that Mg doping triggers an onset of α- to β-phase structural transition in Cu2−x Mg x V2O7 above a critical Mg concentration x c = 0.15, and both the phases coexist up to x = 0.25. Cu2V2O7 possesses a non-centrosymmetric crystal structure and antiferromagnetic ordering along with a non-collinear spin structure in the α phase, originated from the microscopic Dzyaloshinskii–Moriya interaction between the neighboring Cu spins. Accordingly, a weak ferromagnetic (FM) behavior has been observed up to x = 0.25. However, beyond this concentration, Cu2−x Mg x V2O7 exhibits complex magnetic properties. A clear dielectric anomaly is observed in α–Cu2−x Mg x V2O7 around the magnetic transition temperature, which loses its prominence with the increase in Mg doping. The analysis of experimental data shows that the magnetoelectric coupling is nonlinear, which is in agreement with the Landau theory of continuous phase transitions. Co doping, on the other hand, initiates a sharp α to β phase transition around the same critical concentration x c = 0.15 in Cu2−x Co x V2O7 but the FM behavior is very weak and can be detected only up to x = 0.10. We have drawn the magnetic phase diagram which indicates that the rate of suppression in transition temperature is the same for both types of doping, magnetic (Co) and nonmagnetic (Zn/Mg).

Van der Waals fluid and charged AdS black hole in the Landau theory

By introducing the general construction of Landau functional of the van der Waals system and charged AdS black hole system, we have preliminarily realized the Landau continuous phase transition theory in black hole thermodynamics. The results show that the Landau functional constructed in present paper can directly reflect the physical process of black hole phase transition. Specifically, the splitting of the global minimum of the Landau functional corresponds to the second-order phase transition of the black hole, and the transformation of the global minimum reflects the first-order phase transition of the black hole.

Microstructure and continuous phase transition of a regular Hayward black hole in anti-de Sitter spacetime

Abstract In this article we study the thermodynamic phase transition of a regular Hayward-AdS black hole, by introducing a new order parameter, which is the potential conjugate to the magnetic charge arising from a non-linearly coupled electromagnetic field. We use Landau continuous phase transition theory to discuss the van der Waals-like critical phenomena of the black hole. The well-known interpretation of the phase transition of an AdS black hole as being a large and small black hole transition is re-interpreted as being a transition between a high-potential phase and a low-potential phase. The microstructure associated with this phase transition is studied using the Ruppeiner geometry. By investigating the behaviour of the Ruppeiner scalar curvature, we find that charged and uncharged (effective) molecules of the black hole have distinct microstructure, which is analogous to that of fermion and boson gas.

Ehrenfest’s scheme and microstructure for regular-AdS black hole in the extended phase space

The regular (Bardeen)–anti-de Sitter (AdS) (BAdS) black hole (BH) in the extended phase space is taken as an example for investigating the BH phase transition grade from both macroscopic and microscopic points of view. The equation of state and thermodynamic quantities of this BH are obtained. It is found that the BAdS BH phase space in the extended phase space should be a second-order phase transition near the critical point by verifying the Ehrenfest’s equation, and the possibility of its first-order phase transition can be ruled out by the entropy continuity and the heat capacity mutation. The critical exponents from the microscopic structure are analytically and numerically presented with the Landau continuous phase transition theory by introducing a microscopic order-parameter.

Continuous phase transition and microstructure of charged AdS black hole with quintessence

Previously, the Maxwell equal-area law has been used to discuss the conditions satisfied by the phase transition of charged AdS black holes with cloud of string and quintessence, and it was concluded that black holes have phase transition similar to that of vdW system. The phase transition depends on the electric potential of the black hole and is not the one between a large black hole and a small black hole. On the basis of this result, we study the relation between the latent heat of the phase transition and the parameter of dark energy, and use the Landau continuous phase transition theory to discuss the critical phenomenon of the black hole with quintessence and give the critical exponent. By introducing the number density of the black hole molecules, some properties of the microstructure of black holes are studied in terms of a phase transition. It is found that the electric charge of the black hole and the normalization parameter related to the density of quintessence field play a key role in the phase transition. By constructing the binary fluid model of the black hole molecules, we also discuss the microstructure of charged AdS black holes with a cloud of strings and quintessence.

Microstructure and continuous phase transition of a Reissner-Nordstrom-AdS black hole

As is well known that RN-AdS black hole has a phase transition which is similar to that of van der Waals system. The phase transition depends on the electric potential of the black hole and is not the one between a large black hole and a small black hole. On this basis, we introduce a new order parameter and use the Landau continuous phase transition theory to discuss the critical phenomenon of RN-AdS black hole and give the critical exponent. By constructing the binary fluid model of black hole molecules, we investigate the microstructure of black holes. Furthermore, by studying the effect of the spacetime scalar curvature on the phase transition, we find that the charged and uncharged molecules of black holes are with different microstructure red which is like fermion gas and boson gas.

Modeling Deformation Wave in Rock Mass near Deep-Level Tunnel

In this paper deformation wave is studied on the basis of continuous phase transition theory. Relative shear strain is taken as an order parameter. The potential energy is obtained by analogy with the Ginzburg–Landau expansion of free energy. Hamilton’s variational principle is used to obtain the motion equation by which several types of deformation waves can be modeled. The results show that the proposed model is effective in modeling deformation waves.

Green Function Calculations of Properties for the Magnetocaloric Layered Structures Based Upon FeMnAsP

The alternating Fe–Mn layered structures of the compounds FeMnAsxP[Formula: see text] display properties which have been demonstrated experimentally as very promising as far as commercial applications of the magnetocaloric effect are concerned. However, the theoretical literature on this and other families of magnetocaloric compounds still adopts simple molecular-field models in the description of important statistical mechanical properties like the entropy variation that accompanies applied isothermal magnetic field cycling, as well as the temperature variation following adiabatic magnetic field cycles. In the present paper, a random phase approximation Green function theoretical treatment is applied to such structures. The advantages of such approach are well known since the details of the crystal structure are easily incorporated in the model, as well as a precise description of correlations between neighbor spins can be obtained. We focus on a simple one-exchange parameter Heisenberg model, and the observed first-order phase transitions are reproduced by the introduction of a biquadratic term in the Hamiltonian whose origin is related both to the magnetoelastic coupling with the phonon spectrum in these compounds as well as with the values of spins in the Fe and Mn ions. The calculations are compared with experimental magnetocaloric data for the FeMnAsxP[Formula: see text] compounds. In particular, the magnetic field dependence for the entropy variation at the transition temperature predicted from the Landau theory of continuous phase transitions is reproduced even in the case of discontinuous transitions.

Modeling the zonal disintegration of rocks near deep level tunnels by gradient internal variable continuous phase transition theory

AbstractThe occurrence of alternating damage zones surrounding underground openings (commonly known as zonal disintegration) is treated as a “far from thermodynamic equilibrium” dynamical process or a nonlinear continuous phase transition phenomenon. The approach of internal variable gradient theory with diffusive transport, which may be viewed as a subclass of Landau’s phase transition theory, is adopted. The order parameter is identified with an irreversible strain quantity, the gradient of which enters into the expression for the free energy of the rock system. The gradient term stabilizes the material behavior in the post-softening regime, where zonal disintegration occurs. The results of a simplified linearized analysis are confirmed by the numerical solution of the nonlinear problem.

Non-equilibrium universality in the dynamics of dissipative cold atomic gases

The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The well-established concept at or near equilibrium, universality, can also characterize the physics of systems out of equilibrium. The most fundamental instance of a genuine non-equilibrium phase transition is the directed percolation (DP) universality class, where a system switches from an absorbing inactive to a fluctuating active phase. Despite being known for several decades it has been challenging to find experimental systems that manifest this transition. Here we show theoretically that signatures of the DP universality class can be observed in an atomic system with long-range interactions. Moreover, we demonstrate that even mesoscopic ensembles—which are currently studied experimentally—are sufficient to observe traces of this non-equilibrium phase transition in one, two and three dimensions.

Finite-temperature properties of N two-level atoms in a single-mode optic cavity and phase transition

In this paper, we investigate the finite-temperature properties and phase transition of the Dicke model. Converting the atomic pseudo-spin operator to the two-mode Fermi operators, we obtain the partition function in terms of the imaginary-time path integral. The atomic population and average photon number as analytic functions of the atom-photon coupling strength are found from the thermodynamic equilibrium equation, which leads to the stationary state at a finite temperature and is determined by the variation in an extremum-condition of the Euclidean action with respect to the bosonic field. In particular we study the phase transition from normal to superradiation phase at a fixed low-temperature, in which the phase transition is dominated by quantum fluctuations. The phase transition induced by the variation of the atom-photon coupling strength indeed obeys the Landau continuous phase-transition theory, in which the average photon-number can serve as an order parameter with non-zero value that characterizes the superradiation phase. In the zero temperature limit our results recover exactly all those obtained from the quantum phase transition theory at zero temperature. In addition, we discuss the thermodynamic properties and compare the difference between finite-temperature phase transition and zero-temperature quantum phase transition. It is discovered that the average photon-number and mean energy in the low-temperature stationary state coincide with the corresponding values of zero-temperature in the strong coupling region. The entropy of the superradiation phase decays rapidly to zero with the increase of coupling strength.

Dimensional transitions in small Yukawa clusters

We provide a detailed analysis of structural transitions leading to rapid changes in the dimensionality of small Yukawa clusters. These transformations are induced by variations in the shape of confinement as well as the screening strength. We show that even in the most primitive systems composed of only a few strongly interacting particles, the order parameter exhibits a power-law behavior in the vicinity of the critical point of the continuous transition. The critical exponent γ = 1/2 is found to be universal in all studied cases, which is consistent with the general theory of continuous phase transitions.

Finite-size scaling analysis of isotropic–polar phase transitions in an amphiphilic fluid

We present Monte Carlo simulations of the isotropic–polar (IP) phase transition in an amphiphilic fluid carried out in the isothermal–isobaric ensemble. Our model consists of Lennard-Jones spheres where the attractive part of the potential is modified by an orientation-dependent function. This function gives rise to an angle dependence of the intermolecular attractions corresponding to that characteristic of point dipoles. Our data show a substantial system-size dependence of the dipolar order parameter. We analyze the system-size dependence in terms of the order-parameter distribution and a cumulant involving its first and second moments. The order parameter, its distribution, and susceptibility observe the scaling behavior characteristic of the 3D Ising universality class. Because of this scaling behavior and because all cumulants have a common intersection irrespective of system size we conclude that the IP phase transition is continuous. Considering pressures 1.3 ≤ P ≤ 3.0 we demonstrate that a line of continuous phase transitions exists which is analogous to the Curie line in systems exhibiting a ferroelectric transition. Our results are qualitatively consistent with Landau’s theory of continuous phase transitions.

A model for the relationship between tropical precipitation and column water vapor

Several observational studies have shown a tight relationship between tropical precipitation and column‐integrated water vapor. We show that the observed relationship in the tropics between column‐integrated water vapor, precipitation, and its variance can be qualitatively reproduced by a simple and physically motivated two‐layer model. It has previously been argued that features of this relationship could be explained by analogy with the theory of continuous phase transitions. Instead, our model explicitly assumes that the onset of precipitation is governed by a stability threshold involving boundary‐layer water vapor. This allows us to explain the precipitation‐humidity relationship over a broader range of water vapor values, and may explain the observed temperature dependence of the relationship.

Are Guggenheim formulae and Landau theory still applicable to expanded liquid metals?

In the present work, we have found that Guggenheim formulae are still applicable to the liquid–vapor coexistence curves of expanded fluid metals only by adjusting their coefficients rather than exponents. In addition, the equation of state of expanded liquid cesium has been derived based on Landau theory of continuous phase transitions including the sixth-order term of the order parameter. Both the equation of state and the coexistence curves obtained are in good agreement with experimental data.

Correlated one-body density matrix of boson superfluids

The correlated density matrix theory is employed and further developed to analyze the one-body density matrix ρ1(|r1-r2|) of the normal and superfluid phases of a strongly interacting Bose system at non-zero temperature. The approach continues the formal development described in an earlier article and is based on a suitable trial ansatz for the many-body density matrixW(R, R′)∼Φ(R) Q(R, R′) Φ(R′) with the wave function Φ and incoherence factorQ incorporating the essential statistical and dynamical correlations. Special attention is given to the appearance of off-diagonal long-range order in function ρ1(|r1-r2|) and its relation to the condensation strength Bcc characterizing the degree of coherence in the superfluid phase. We derive a number of structural relations that have counterparts in known results on ρ1 in the Jastrow variational theory of the Bose ground state. We discuss Bose-Einstein condensation and make contact to Landau's phenomenological theory of continuous phase transitions. Numerical estimates are presented on the condensation strength and the condensate fraction of liquid4He as functions of the temperature.

Are there two length scales at phase transitions?

The development of high resolution x-ray scattering techniques, particularly using synchrotron sources enables very detailed measurements of the properties of the fluctuations associated with continuous phase transitions. Surprisingly, the results of almost all high resolution studies of structural and magnetic phase transitions in crystals show that two length scales are needed to describe the experimental results in striking contradiction to the basic hypothesis of the scaling theory of continuous phase transitions. The measurements further suggest that the longer length scale arises from a region of the crystal close (50 μm) to the surface.Possible explanations for the two length scale behaviour will be discussed including the effects of surface damage, the effects of surface strains, or intrinsic behaviour and some experiments outlined which might distinguish between these different possibilities.