Phase Transition Line Research Articles

Hybrid Berezinskii-Kosterlitz-Thouless and Ising topological phase transition in the generalized two-dimensional XY model using tensor networks

In tensor network representation, the partition function of a generalized two-dimensional XY spin model with topological integer and half-integer vortex excitations is mapped to a tensor product of one-dimensional quantum transfer operator, whose eigenequation can be solved by an algorithm of variational uniform matrix product states. Using the singularities of the entanglement entropy, we accurately determine the complete phase diagram of this model. Both the integer vortex-antivortex binding and half-integer vortex-antivortex binding phases are separated from the disordered phase by the usual Berezinskii-Kosterlitz-Thouless (BKT) transitions, while a continuous topological phase transition exists between two different vortex binding phases, exhibiting a logarithmic divergence of the specific heat and exponential divergence of the spin correlation length. A hybrid BKT and Ising universality class of topological phase transition is thus established. We further prove that three phase transition lines meet at a multicritical point from which a deconfinement crossover line extends into the disordered phase.

Magnetic phase transitions in two-dimensional two-valley semiconductors with in-plane magnetic field

A two-dimensional electron gas (2DEG) in two-valley semiconductors has two discrete degrees of freedom given by the spin and valley quantum numbers. We analyze the zero-temperature magnetic instabilities of two-valley semiconductors with SOI, in-plane magnetic field, and electron-electron interaction. The interplay of an applied in-plane magnetic field and the SOI results in non-collinear spin quantization in different valleys. Together with the exchange intervalley interaction this results in a rich phase diagram containing four non-trivial magnetic phases. The negative non-analytic cubic correction to the free energy, which is always present in an interacting 2DEG, is responsible for first order phase transitions. Here, we show that non-zero ground state values of the order parameters can cut this cubic non-analyticity and drive certain magnetic phase transitions second order. We also find two tri-critical points at zero temperature which together with the line of second order phase transitions constitute the quantum critical sector of the phase diagram. The phase transitions can be tuned externally by electrostatic gates or by the in-plane magnetic field.

The phase diagram of ultra quantum liquids

We discuss the dependence of the phase diagram of a hypothetical isotope of helium with nuclear mass less than 4 atomic mass units. We argue that with decreasing nucleus mass, the temperature of the superfluid phase transition (about 2.2 K in real 4He) increases, while that of the liquid–gas critical point (about 5.2 K in real 4He) decreases. We discuss various scenarios that may occur when the two temperatures approach each other and the order parameters of the superfluid and the liquid–gas phase transitions interact with each other. The simplest scenario, in which both order parameters become critical at particular values of the nuclear mass, temperature, and pressure, can be ruled out through on an analysis of the Landau theory. We argue that in the most likely scenario, as the nuclear mass decreases, first, a tricritical point appears on the line separating the superfluid and the normal fluid phase, then the critical point disappears under the first-order part of superfluid phase transition line, and in the end the tricritical point disappears. The last change in the phase diagram occurs when the two-body scattering length crosses zero, which corresponds to the nuclear mass of about 1.55 u. We develop a quantitative theory that allows one to determine the phase diagram in the vicinity of this point. Finally, we discuss several ways to physically realize such liquids.

Overview of fluctuation and correlation measurements

One of the ultimate goals of nuclear collision experiments at high energy is to map the phase diagram of strongly interacting matter. A very challenging task is the determination of the QCD phase structure including the search for critical behavior and verification of the possible existence of a critical end point of a first order phase transition line. A promising tool to probe the presence of critical behavior is the study of fluctuations and correlations of conserved charges since, in a thermal system, these fluctuations are directly related to the equation of state (EoS) of the system under the study. In this report an overview is given of several experimental measurements on net-proton multiplicity distributions such as cumulants and multi-particle correlation functions.

Molecular model for nematic, smectic-A, and smectic-C liquid crystals.

We analyze a molecular model to describe the phase transitions between the isotropic, nematic, smectic-A, and smectic-C phases. The smectic phases are described by the use of a pair potential, which lacks the full rotational symmetry because of the cylindrical symmetry around the smectic axis. The tilt of the long molecules inside the smectic layers is favored by a biquadratic pair potential, which compete with the pair potential of the McMillan model. The part of the phase diagram showing the first three phases is similar to that of the McMillan molecular model. The smectic-C phase is separated from the nematic by a continuous phase transition line along which the tilt angle is nonzero. The tilt angle vanishes continuously when one reaches the line separating the smectic-C and the smectic-A line.

Mayer group expansion for solids: Application to polymorphic transition in highly compressed nitrogen

The Mayer group expansion for solids proposed earlier is applied in prediction of the location of polymorphic phase transition line between the cubic and layered phases of polymeric nitrogen. The comparison with existing measurements revealed that theoretical calculations based on the proposed potential model calibrated on ab initio energy calculations are in agreement with existing experimental data. Predicted location of the polymorphic transition line and specific behavior of thermal properties of both phases in a wide temperature range is discussed.

Easy-hard phase transition in parameter estimation for optical waveguides

The determination of the parameters of cylindrical optical waveguides, e.g. the diameters vec {d}=(d_1,ldots ,d_r) of r layers of (semi-) transparent optical fibres, can be executed by inverse evaluation of the scattering intensities that emerge under monochromatic illumination. The inverse problem can be solved by optimising the mismatch R(vec {d}) between the measured and simulated scattering patterns. The global optimum corresponds to the correct parameter values. The mismatch R(vec {d}) can be seen as an energy landscape as a function of the diameters. In this work, we study the structure of the energy landscape for different values of the complex refractive indices vec {n}, for r=1 and r=2 layers. We find that for both values of r, depending on the values of vec {n}, two very different types of energy landscapes exist, respectively. One type is dominated by one global minimum and the other type exhibits a multitude of local minima. From an algorithmic viewpoint, this corresponds to easy and hard phases, respectively. Our results indicate that the two phases are separated by sharp phase-transition lines and that the shape of these lines can be described by one “critical” exponent b, which depends slightly on r. Interestingly, the same exponent also describes the dependence of the number of local minima on the diameters. Thus, our findings are comparable to previous theoretical studies on easy-hard transitions in basic combinatorial optimisation or decision problems like Travelling Salesperson and Satisfiability. To our knowledge our results are the first indicating the existence of easy-hard transitions for a real-world optimisation problem of technological relevance.

Landau theory for non-symmetry-breaking electronic instability coupled to symmetry-breaking order parameter applied to Prussian blue analog

Different types of ordering phenomena may occur during phase transitions, described within the universal framework of the Landau theory through the evolution of one, or several, symmetry-breaking order parameter h. In addition, many systems undergo phase transitions related to an electronic instability, in the absence of a symmetry-breaking and eventually described through the evolution of a totally symmetric order parameter q linearly coupled to volume change. Analyzing the coupling of a non-symmetry-breaking electronic instability, responsible for volume strain, to symmetry-breaking phenomena is of importance for many systems in nature and here we show that the symmetry-allowed qh2 coupling plays a central role. We use as case study the rubidium manganese hexacyanoferrate Prussian blue analogue, exhibiting phase transitions with hysteresis that may exceed 100 K, and based on intermetallic charge transfer (CT). During the phase transition, the intermetallic CT described through the evolution of q is coupled to cubic-tetragonal ferroelastic symmetry-breaking described through the evolution of h. In this system, the symmetry-breaking and non-symmetry breaking deformations have similar amplitudes but the large volume strain is mainly due to CT. We analyze both the ferroelastic and the CT features of the phase transition within the frame of the Landau theory, taking into account the qh2 coupling, stabilizing concomitant CT and Jahn-Teller distortion. The phase diagrams obtained with this model are in good qualitative agreement with various experimental findings and apply to diverse families of materials undergoing Mott transition, spin-crossover, neutral-ionic transition, for which isostructural electronic instability driving volume strain can couple to symmetry-breaking or not, create phase transition lines and drive cooperative phenomena.

Research on the yield function of sand based on thermodynamics

It is well known that stress-strain relation of sand is influenced by anisotropic fabric. In this paper, the relationship between macroscopic strain and shear strain and its pore structure is established by combining micromechanical theory and pore structure tensor. It is further confirmed that the stress-induced anisotropy and dilatancy of sand are inevitable. Based on this, with the help of thermodynamic theory, the inclined elliptic yield surface function in dissipative space is built, and there are three important lines in dissipative space for the influence of anisotropic fabric, normal consolidation line, phase transition line and peak line respectively corresponding to the three characteristic lines of real stress space: normal consolidation line, phase transition line and peak line which really reflects the mechanical properties of sand, especially dense sand.

One-dimensional cell motility patterns

During migration cells exhibit a rich variety of seemingly random migration patterns, which makes unraveling the underlying mechanisms that control cell migration a daunting challenge. For efficient migration cells require a mechanism for polarization, so that traction forces are produced in the direction of motion, while adhesion is released to allow forward migration. To simplify the study of this process cells have been studied when placed along one-dimensional tracks, where single cells exhibit both smooth and stick-slip migration modes. The stick-slip motility mode is characterized by protrusive motion at the cell front, coupled with slow cell elongation, which is followed by rapid retractions of the cell back. In this study, we explore a minimal physical model that couples the force applied on the adhesion bonds to the length variations of the cell and the traction forces applied by the polarized actin retrograde flow. We show that the rich spectrum of cell migration patterns emerges from this model as different \emph{deterministic} dynamical phases. This result suggests a source for the large cell-to-cell variability (CCV) in cell migration patterns observed in single cells over time and within cell populations. The large heterogeneity can arise from small fluctuations in the cellular components that are greatly amplified due to moving the cells' internal state across the dynamical phase transition lines. Temporal noise is shown to drive random changes in the cellular polarization direction, which is enhanced during the stick-slip migration mode. These results offer a new framework to explain experimental observations of migrating cells, resulting from noisy switching between underlying deterministic migration modes.

Spin-1 Ising model with nearest and next-nearest bilinear and biquadratic interactions on the Bethe lattice

The spin-1 Ising model is examined on the Bethe lattice (BL) by considering the effects of nearest and next-nearest neighbor bilinear (J) and biquadratic (K) exchange interactions on a honeycomb lattice. The exact recursion relations (ERR) are employed in the double-shell approximation to obtain the order-parameters. The phase diagrams of the model are obtained from the thermal analysis of the order-parameters. The phase transition lines separating the different phase regions, i.e. ferromagnetic (FM), antiferromagnetic (AFM), paramagnetic (PM) and chaotic, are calculated. The chaotic phase regions are especially interesting which is usually observed when the system presents phase transitions from AFM to FM phases.

Bridging transitions and capillary forces for colloids in a slit.

Capillary bridges can form between colloids immersed in a two-phase fluid, e.g., in a binary liquid mixture, if the surface of the colloids prefers the species other than the one favored in the bulk liquid. Here, we study the formation of liquid bridges induced by confining colloids to a slit, with the slit walls having a preference opposite to the one of the colloid surface. Using mean field theory, we show that there is a line of first-order phase transitions between the bridge and the no-bridge states, which ends at a critical point. By decreasing the slit width, this critical point is shifted toward smaller separations between the colloids. However, at very small separations and far from criticality, we observe only a minor influence of the slit width on the location of the transition. Monte Carlo simulations of the Ising model, which mimics incompressible binary liquid mixtures, confirm the occurrence of the bridging transitions, as manifested by the appearance of "spinodal" regions where both bridge and no-bridge configurations are stable or metastable. Interestingly, we find that there is no such spinodal region in the case of small colloids, but we observe a sharpening of the transition when the colloid size increases. In addition, we demonstrate that the capillary force acting between the colloids can depend sensitively on the slit width and varies drastically with temperature, thus achieving strengths orders of magnitude higher than at criticality of the fluid.

Tricritical Physics in Two-Dimensional p-Wave Superfluids.

We study effects of quantum fluctuations on two-dimensional p+ip superfluids near resonance. In the standard paradigm, phase transitions between superfluids and zero density vacuum are continuous. When strong quantum fluctuations near resonance are present, the line of continuous phase transitions terminates at two tricritical points near resonance, between which the transitions are expected to be first-order ones. The size of the window where first-order phase transitions occur is shown to be substantial when the coupling is strong. Near first-order transitions, superfluids self-contract due to phase separations between superfluids and vacuum.

The effect of film thickness on the modulated spin structure of terbium manganite

The Ginzburg–Landau method is used to conduct a phenomenological analysis of how the sample thickness impacts the incommensurate spin states in the TbMnO3 centrosymmetric ferroelectromagnet. The analysis is performed using the first-harmonic approximation, and provides a qualitative confirmation of the experimentally observed decrease in the film modulation vector at a decreasing temperature, as well as an increase in the vector as the film thickness decreases at a constant temperature. The effect that the film thickness has on the first- and second-order phase transition lines is analyzed, and the tendency of the incommensurate spin phase volume to decrease with a decrease in the film thickness is demonstrated.

Analysis of interactions in totally asymmetric exclusion process with site-dependent hopping rates: theory and simulations

Biological molecular motors are special enzymes that support biological processes such as intracellular transport, vesicle locomotion, RNA translation and many more. Experimental works suggest that the motor proteins interact among each other and moreover they experience a push by other motors during the intracellular transport. To incorporate these dynamics, we consider a variant of open one-dimensional totally asymmetric simple exclusion process with site-dependent hopping rates and interactions. The qualitative properties of our system do not depend on the hopping rate function. We utilize the simple mean-field, the cluster mean-field, the correlated cluster mean-field to theoretically calculate the stationary phase diagrams, density and the maximal particle current. The limitations of all the three theories are extensively discussed. It has been found that although the interactions do not change the number of phases in a phase diagram, it significantly changes the density profiles, the phase transition lines and the maximal particle current. The theoretical results obtained are supported by Monte Carlo simulations.

Reduction of energy-gap scaling by coherent catalysis in models of quantum annealing

Non-stoquastic drivers are known to improve the performance of quantum annealing by reducing first-order phase transitions into second-order ones in several mean-field-type model systems. Nevertheless, statistical-mechanical analysis shows that some target Hamiltonians still exhibit unavoidable first-order transitions even with non-stoquastic drivers, making them difficult for quantum annealing to solve. Recently, a mechanism called coherent catalysis was proposed by Durkin [Phys. Rev. A \textbf{99}, 032315 (2019)], in which he showed the existence of a particular point on the line of first-order phase transitions where the energy gap scales polynomially as expected for a second-order transition. We show by extensive numerical computations that this phenomenon is observed in a few additional mean-field-type optimization problems where non-stoquastic drivers fail to change the order of phase transition in the thermodynamic limit. This opens up the possibility of using coherent catalysis to search for exponential speedups in systems previously thought to be exponentially slow for quantum annealing to solve.

Tuning the two-step melting of magnetic order in a dipolar kagome spin ice by quantum fluctuations

Complex magnetic orders in frustrated magnets may exhibit rich melting processes when the magnet is heated toward the paramagnetic phase. We show that one may tune such melting processes by quantum fluctuations. We consider a kagome lattice dipolar Ising model subject to transverse field and focus on the thermal transitions out of its magnetic ground state, which features a $\sqrt{3}\times\sqrt{3}$ magnetic unit cell. Our quantum Monte Carlo (QMC) simulations suggest that, at weak transverse field, the $\sqrt{3}\times\sqrt{3}$ phase melts by way of an intermediate magnetic charge ordered phase where the lattice translation symmetry is restored while the time reversal symmetry remains broken. By contrast, at stronger transverse field, QMC simulations suggest the $\sqrt{3}\times\sqrt{3}$ phase melts through a floating Kosterlitz-Thouless phase. The two distinct melting processes are separated by either a multicritical point or a short line of first order phase transition.

APPLICATION OF GEOMETROTHERMODYNAMICS TO THE SYSTEM WITH ZERO SOUND DESCRIBED BY THE METHOD OF HOLOGRAPHIC DUALITY

In the framework of the method of geometrothermodynamics, in present work, we studied the properties of equilibrium manifold of the system with zero-sound predicted by the holographic duality method. The results are invariant under the Legendre transformations, i.e. independent of the choice of thermodynamic potential. For the systems under consideration, the corresponding metrics, determinants of metrics and scalar curvatures are calculated, and their properties are also described. Using the holographic approach, a new type of quantum liquid was discovered. The heat capacity of the liquid obtained in this work at low temperatures depends on the temperature ∼ T6. Entropy, which depends on temperature and baryom density, was taken as the thermodynamic potential. 3-dimensional obtained that clearly show at which values of thermodynamic variables scalar curvatures tend to infinity or to zero, which indicates possible phase transitions and possible compensation of interactions by quantum effects, respectively. It is shown that both variants of metrics in this case lead to the same conclusion regarding the location of possible phase transition lines in the considered holographic system with zero sound.

Quarkyonic phase from quenched dynamical holographic QCD model

Chiral and deconfinement phase transitions at finite temperature T and quark number chemical potential μ are simultaneously studied in the quenched dynamical holographic QCD model within the Einstein-Dilaton-Maxwell framework. By calculating the corresponding order parameters, i.e., the chiral condensate and Polyakov loop, it is shown that the transition lines of these two phase transitions are separated in the T − μ plane. The deconfinement phase transition is shown to be always of crossover type and the transition line depends weakly on the baryon number density. Differently, the chiral transition is of crossover at small baryon number density and it turns to be of first order at sufficient large baryon number density. A critical endpoint (CEP), at which the transition becomes second order type, appears in the chiral transition line. This is the first time to realize the CEP of chiral phase transition in the (T, μ) plane using the holographic EMD (Einstein-Maxwell-Dilaton) model for two flavour case. It is observed that between these two phase transition lines, there is a region with chiral symmetry restored and color degrees still confined, which could be considered as the quarkyonic phase. Qualitatively, this behavior is in consistent with the result in the Polyakov-loop improved Nambu-Jona-Lasinio (PNJL) model.

Numerical Simulation of Finite-Temperature Field Theory for Interacting Bosons.

We report a stable and efficient complex Langevin sampling scheme for performing approximation-free numerical simulations directly on the path-integral coherent-states field theory for an assembly of interacting bosons. We apply the method to generate the λ line of critical phase transitions associated with Bose-Einstein condensation in a model ϕ^{4} scalar field theory. The new approach enjoys near-linear scaling in the resolved (d+1) spatial and imaginary-time dimensions and should be particularly efficient for the study of dense systems at low temperature.