Line Of First-order Phase Transitions Research Articles

Fully polarized Fermi systems at finite temperature.

We propose a simple model of an interacting, fully spin-polarized Fermi gas in dimensions d=2 and d=3, and derive the approximate expression for the energy spectrum and the corresponding formula for the Helmholtz free energy. We analyze the thermodynamics of the system and find the lines of first-order phase transitions between the low- and high-density phases terminating at critical points. The properties of the corresponding phase diagrams are qualitatively different for d=2 and 3, and sensitively depend on the interparticle attraction, which marks a departure from the standard van der Waals theory. The differences originate from the Pauli exclusion principle and are embedded in the fermionic nature of the system under study.

On the accuracy of the Clausius-Clapeyron relation

It was shown that the Clausius-Clapeyron relation (CCR) determines only the maximum possible slope of the first-order phase transition (PT-1) line in the temperature-pressure coordinates. This conclusion follows from the fact that the real PT-1 it is an irreversible process. An inequality has been obtained that generalizes the CCR to the case of irreversibility at PT-1: the Clausius-Clapeyron inequality (CCI). It is indicated that the CCI passes into equality (i.e., into the CCR) only in the case of reversible PT-1. Analysis of experimental data for various types of PT-1 showed the implementation of CCI in most cases. Herewith, the deviation from the CCR is the more noticeable, the greater the volume change in PT-1. It was found that deviations of experimental data from the CCR correlate with the presence of phase-transition radiation in PT-1. This makes it possible to use the value of the deviation from the CCR for thermodynamic indication of the probability of observing phase-transition radiation at PT-1 in various substances. A method has been proposed for estimating the irreversibility PT-1 value, based on the magnitude of the deviation from the CCR. The obtained CCI has been generalized to the case of the presence of an external homogeneous magnetic (or electric) field acting on the two phases of matter in equilibrium.

The finite volume effects on the critical endpoint of chiral phase transition in Nambu–Jona-Lasinio model with different regularization schemes

In this paper, we study the influence of different regularization schemes on the critical endpoint (CEP) of chiral phase transition within a cubic box with volume [Formula: see text]. A two-flavor Nambu–Jona-Lasinio model at finite temperature [Formula: see text] and chemical potential [Formula: see text] is adopted as the effective model of the strong interacting matter. Due to the finite volume of the box, the momentum integral in gap equation is replaced by discrete summation, and an anti-periodic boundary condition for quark field is applied. We employ the Schwinger’s proper time and the Pauli–Villars regularization (PVR) schemes, respectively. It is found that the first-order phase transition line displays an intriguing “staircase” behavior, and eventually disappears as [Formula: see text] increases. In particular, there is no existence of the CEP for both regularization schemes in infinite volume limit [Formula: see text]. However, for the finite volume, the locations of the CEPs with proper time and PVR are determined, respectively.

Thermodynamic determination of the equilibrium first-order phase-transition line hidden by hysteresis in a phase diagram

In some materials exhibiting field-induced first-order transitions (FOTs), the equilibrium phase-transition line is hidden by the hysteresis region associated with the FOT. In general, phase diagrams form the basis for the study of material science, and the profiles of phase-transition lines separating different thermodynamic phases include comprehensive information about thermodynamic quantities, such as latent heat. However, in a field-induced FOT, the equilibrium phase-transition line cannot be precisely determined from measurements of resistivity, magnetization, etc, especially when the transition is accompanied by large hysteresis. Here, we demonstrate a thermodynamics-based method for determining the hidden equilibrium FOT line in a material exhibiting a field-induced FOT. This method is verified for the field-induced FOT between antiferromagnetic and ferrimagnetic states in magneto-electric compounds (text {Fe}_{0.95}text {Zn}_{0.05})_{2}text {Mo}_{3}hbox {O}_{8}. The equilibrium FOT line determined based on the Clausius–Clapeyron equation exhibits a reasonable profile in terms of the third law of thermodynamics, and it shows marked differences from the midpoints of the hysteresis region. Our findings highlight that for a field-induced FOT exhibiting large hysteresis, care should be taken for referring to the hysteresis midpoint line when discussing field-induced latent heat or magnetocaloric effects.

Phase diagram of holographic thermal dense QCD matter with rotation

We study the rotation effects of the hot and dense QCD matter in a non-perturbative regime by the gauge/gravity duality. We use the gravitational model that is designated to match the state-of-the-art lattice data on the thermal properties of (2+1)-flavor QCD and predict the location of the critical endpoint and the first-order phase transition line at large baryon chemical potential without rotation. After introducing the angular velocity via a local Lorentz boost, we investigate the thermodynamic quantities for the system under rotation in a self-consistent way. We find that the critical temperature and baryon chemical potential associated with the QCD phase transition decrease as the angular velocity increases. Moreover, some interesting phenomena are observed near the critical endpoint. We then construct the 3-dimensional phase diagram of the QCD matter in terms of temperature, baryon chemical potential, and angular velocity. As a parallel investigation, we also consider the gravitational model of SU(3) pure gluon system, for which the 2-dimensional phase diagram associated with temperature and angular velocity has been predicted. The corresponding thermodynamic quantities with rotation are investigated.

Euclidean dynamical triangulations revisited

We conduct numerical simulations of a model of four-dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume, the model contains a discrete Einstein-Hilbert term with coupling $\ensuremath{\kappa}$ and a local measure term with coupling $\ensuremath{\beta}$ that weights triangulations according to the number of simplices sharing each vertex. We map out the phase diagram in this two-dimensional parameter space and compute a variety of observables that yield information on the nature of any continuum limit. Our results are consistent with a line of first-order phase transitions with a latent heat that decreases as $\ensuremath{\kappa}\ensuremath{\rightarrow}\ensuremath{\infty}$. We find a Hausdorff dimension along the critical line that approaches ${D}_{H}=4$ for large $\ensuremath{\kappa}$ and a spectral dimension consistent with ${D}_{s}=\frac{3}{2}$ at short distances. These results are broadly in agreement with earlier works on Euclidean dynamical triangulation models which utilize degenerate triangulations and/or different measure terms and indicate that such models exhibit a degree of universality.

Phases of the spin- 12 Heisenberg antiferromagnet on the diamond-decorated square lattice in a magnetic field

The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a ferrimagnetic regime. Using a combination of analytical arguments, density matrix renormalization group (DMRG), exact diagonalization as well as sign-problem-free quantum Monte Carlo (QMC) calculations, we investigate the properties of this system and the related Lieb lattice in the presence of a finite magnetic field, addressing both the ground-state phase diagram as well as several thermodynamic properties. In addition to the zero-field ground states, we find at high magnetic field a spin-canted phase with a continuously rising magnetization for increasing magnetic field strength as well as the fully polarized paramagnetic phase. At intermediate field strength, we identify a first-order quantum phase transition line between the ferrimagnetic and the monomer-dimer regime. This first-order line extends to finite temperatures, terminating in a line of critical points that belong to the universality class of the two-dimensional Ising model.

Thermal critical points from competing singlet formations in fully frustrated bilayer antiferromagnets

We examine the ground-state phase diagram and thermal phase transitions in a plaquettized fully frustrated bilayer spin-1/2 Heisenberg model. Based on a combined analysis from sign-problem free quantum Monte Carlo simulations, perturbation theory, and free-energy arguments, we identify a first-order quantum phase transition line that separates two competing quantum-disordered ground states with dominant singlet formations on interlayer dimers and plaquettes, respectively. At finite temperatures, this line extends to form a wall of first-order thermal transitions, which terminates in a line of thermal critical points. From a perturbative approach in terms of an effective Ising model description, we identify a quadratic suppression of the critical temperature scale in the strongly plaquettized region. Based on free-energy arguments we furthermore obtain the full phase boundary of the low-temperature dimer-singlet regime, which agrees well with the quantum Monte Carlo data.

Real-complex quantum phase transition in non-Hermitian disorder-free systems

Localization phenomena and the quantum phase transition are two core concepts of low-dimensional condensed-matter physics. The localization transition problem related to vortex line pinning in superconductors can be studied by mapping it to a real-complex non-Hermitian problem. Its relation to the quantum phase transition has to be discerned. We explore these two phase transitions induced by interactions rather than by the disorder in non-Hermitian systems. It is shown that the phase diagram is divided into the classical and quantum regimes by a characteristic temperature. The classical regime contains topological localization transitions and a tricritical point which connects the first-order phase transition line to the second-order transition line. The quantum regime is a nonchaotic and first-order phase transition. In such a quantum regime, the relaxation time does not always satisfy the bound on chaos. We show that the oscillation phase transition line due to quantized Matsubara frequencies can give an index similar in structure to the quantum oscillation in an imaginary magnetic field, which makes the first-order quantum phase diagram behave as a quantum critical phase diagram.

Transport coefficients of the quark-gluon plasma at the critical point and across the first-order line

A bottom-up Einstein-Maxwell-Dilaton holographic model is used to compute, for the first time, the behavior of several transport coefficients of the hot and baryon-rich strongly coupled quark-gluon plasma at the critical point and also across the first-order phase transition line in the phase diagram. The observables under study are of the shear and bulk viscosities, baryon diffusion, thermal conductivity, the jet quenching parameter $\hat{q}$, as well as the heavy-quark drag force and Langevin diffusion coefficients. These calculations provide a phenomenologically promising estimate for these coefficients, given that our model quantitatively reproduces lattice QCD thermodynamics results, both at zero and finite baryon density, besides naturally incorporating the nearly-perfect fluidity of the quark-gluon plasma. We find that the diffusion of baryon charge, and also the shear and bulk viscosities, are suppressed with increasing baryon density, indicating that the medium becomes even closer to perfect fluidity at large densities. On the other hand, the jet quenching parameter and the heavy-quark momentum diffusion are enhanced with increasing density. The observables display a discontinuity gap when crossing the first-order phase transition line, while developing an infinite slope at the critical point. The transition temperatures associated with different transport coefficients differ in the crossover region but are found to converge at the critical point.

Liquid nucleation around charged particles in the vapor phase.

We theoretically investigate the nucleation of liquid droplets from vapor in the presence of a charged spherical particle. Due to field gradients, sufficiently close to the critical pointof the vapor-gas system, the charge destabilizes the vapor phase and initiates a phase transition. The fluid's free energy is described by the van der Waals expression augmented by electrostatic energy and a square-gradient term. We calculate the equilibrium density profile at arbitrary temperatures, particle charges, and vapor densities. In contrast to classical nucleation theory, here, both liquid and vapor phases are different from the bulk phases because they are spatially nonuniform. In addition, the theory applies to both sharp and diffuse interfaces and calculates the surface tension self-consistently. We find the composition profiles and integrate them to get the adsorption near the particle. We find that the adsorption changes discontinuously at a first-order phase transition line. This line becomes a second-order phase transition at high enough temperatures. We describe the transition pointnumerically and provide approximate analytical expressions for it. Similarly to prewetting, the adsorption diverges at the binodal phase boundary. We construct a phase diagram indicating changes in the binodal, spinodal, and critical temperature. It is shown that the field gradient enlarges the range of temperature and vapor density where liquid can nucleate.

Hot and dense quark-gluon plasma thermodynamics from holographic black holes

We present new results on the equation of state and transition line of hot and dense strongly interacting QCD matter, obtained from a bottom-up Einstein-Maxwell-Dilaton holographic model. We considerably expand the previous coverage in baryon densities in this model by implementing new numerical methods to map the holographic black hole solutions onto the QCD phase diagram. We are also able to obtain, for the first time, the first-order phase transition line in a wide region of the phase diagram. Comparisons with the most recent lattice results for the QCD thermodynamics are also presented.

Effects of the random single-ion anisotropy on the spin-1 Blume-Emery-Griffiths model

The Blume-Emery-Griffiths (BEG) model is considered on the Bethe lattice (BL) in terms of exact recursion relations (ERR) under the effect of a crystal field (D) which was either turned on or off randomly for a given probability. The repulsive case of biquadratic exchange interaction ((K < 0)) between the nearest-neighbor (NN) spins is assumed and the effects of changing the coordination number are also investigated. The thermal variation of the order-parameters, i.e. dipole and quadrupole moments, is examined to obtain the phase diagrams. Very rich phase diagrams with the second- and first-order phase transition lines, tricritical, bicritical and critical end points and the occurrence of reentrant behavior are observed. Different phase regions were explored which include the ferromagnetic (F), paramagnetic (P), staggered quadrupolar (SQ) and ferrimagnetic (FI) phases.

Phase transition in the binary mixture of jammed particles with large size dispersity

It has been well established that particulate systems show the jamming transition and critical scaling behaviors associated with it. However, our knowledge is limited to (nearly) monodisperse systems. Recently, a binary mixture of jammed particles with large size dispersity was studied, and it was suggested that two distinct jammed phases appeared. Here, we conduct a thorough numerical study on this system with a special focus on the statistics of and finite-size effects on the fraction of small particles that participate in the rigid network. We present strong evidence that two distinct jammed phases appear depending on the pressure and composition of two species, which are separated by the first-order phase transition. In one of two phases, only large particles are jammed, whereas both small and large particles are jammed in the other phase. We also describe the phase diagram in the pressure-composition plane, where the first-order phase transition line terminates at a critical point. In addition, we investigate the mechanical properties in terms of the elastic moduli over the phase diagram and find that discontinuous changes in elastic moduli emerge across the phase transition. Remarkably, despite the discontinuities, the elastic moduli in each jammed phase exhibit identical scaling laws to those in the monodisperse systems.

Phase diagram for strongly interacting matter in the presence of a magnetic field using the Polyakov–Nambu–Jona-Lasinio model with magnetic field dependent coupling strengths

We study the phase diagram for strongly interacting matter using the 't Hooft determinant extended Nambu--Jona-Lasinio model with a Polyakov loop in the light and strange quark sectors (\emph{up}, \emph{down} and \emph{strange}) focusing on the effect of a magnetic field dependence of the coupling strengths of these interactions. This dependence was obtained so as to reproduce recent lattice QCD results for the magnetic field dependence of the quarks dynamical masses. A finite magnetic field is known to induce several additional first-order phase transition lines with the respective Critical End Points (CEP) in the temperature-quark chemical potential phase diagram when compared to the zero magnetic field case. A study of the magnetic field dependence in the range $eB=0-0.6~\mathrm{GeV}^2$ of the location of these CEPs reveals that the initial one as well as several of the new ones only survive up to a critical magnetic field. Only two remain in the upper limit of the studied magnetic field strength. A comparison of the results obtained with versions of the model with and without Polyakov loop is also done. We also found that the inclusion of the magnetic field dependence on the coupling strengths, while not changing the qualitative features of the phase diagram, affects the location of these CEPs. The comparison of results with and without a regularization cutoff in the medium part of the integrals does not show a significant change.

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.

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.

Vortex phase diagram of rotating superfluid He3−B

We present the first theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid $^3$He-B. Based on a strong-coupling extension of the Ginzburg-Landau theory that accounts for the relative stability of the bulk A and B phases of $^3$He at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid $^3$He-B. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of $H=284\,\mbox{G}$ parallel to the rotation axis, $\vec{H}\parallel\vec{\Omega}$, are reported, as well as the supercooling transition line, $T^{*}_ {v} (p,H)$. In zero field the vortex phases of $^3$He-B are separated by a first-order phase transition line $T_ {v} (p)$ that terminates on the bulk critical line $T_{c}(p)$ at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly-quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and $\beta$ phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, $T^{*}_ {v} (p,H)$, below which it is globally unstable to an array of D-core vortices. For $H\gtrsim 60\,\mbox{G}$ external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating $^3$He-B, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating $^3$He-B.

Locating fixed points in the phase plane.

The critical point is a fixed point in finite-size scaling. To quantify the behavior of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of the width reveals the position of the fixed point, its corresponding phase transition temperature, and scaling exponent ratio. The value of this ratio tells the nature of the fixed point, which can be a critical point, a point of the first-order phase transition line, or a point of the crossover region. To demonstrate the effectiveness of this method, we apply it to three typical samples produced by the three-dimensional three-state Potts model. Results show the method to be more precise and effective than conventional methods. Finally, we discuss a possible application at the Beam Energy Scan program of the Relativistic Heavy Ion Collider.

Thermal tensor network simulations of the Heisenberg model on the Bethe lattice

We have extended the canonical tree tensor network (TTN) method, which was initially introduced to simulate the zero-temperature properties of quantum lattice models on the Bethe lattice, to finite temperature simulations. By representing the thermal density matrix with a canonicalized tree tensor product operator, we optimize the TTN and accurately evaluate the thermodynamic quantities, including the internal energy, specific heat, and the spontaneous magnetization, etc, at various temperatures. By varying the anisotropic coupling constant $\Delta$, we obtain the phase diagram of the spin-1/2 Heisenberg XXZ model on the Bethe lattice, where three kinds of magnetic ordered phases, namely the ferromagnetic, XY and antiferromagnetic ordered phases, are found in low temperatures and separated from the high-$T$ paramagnetic phase by a continuous thermal phase transition at $T_c$. The XY phase is separated from the other two phases by two first-order phase transition lines at the symmetric coupling points $ \Delta=\pm 1$. We have also carried out a linear spin wave calculation on the Bethe lattice, showing that the low-energy magnetic excitations are always gapped, and find the obtained magnon gaps in very good agreement with those estimated from the TTN simulations. Despite the gapped excitation spectrum, Goldstone-like transverse fluctuation modes, as a manifestation of spontaneous continuous symmetry breaking, are observed in the ordered magnetic phases with $|\Delta|\le 1$. One remarkable feature there is that the prominent transverse correlation length reaches $\xi_c=1/\ln{(z-1)}$ for $T\leq T_c$, the maximal value allowed on a $z$-coordinated Bethe lattice.