Line Of First-order Phase Transitions Research Articles

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.

Phases of melonic quantum mechanics

We explore in detail the properties of two melonic quantum mechanical theories which can be formulated either as fermionic matrix quantum mechanics in the new large $D$ limit, or as disordered models. Both models have a mass parameter $m$ and the transition from the perturbative large $m$ region to the strongly coupled "black-hole" small $m$ region is associated with several interesting phenomena. One model, with ${\rm U}(n)^2$ symmetry and equivalent to complex SYK, has a line of first-order phase transitions terminating, for a strictly positive temperature, at a critical point having non-trivial, non-mean-field critical exponents for standard thermodynamical quantities. Quasi-normal frequencies, as well as Lyapunov exponents associated with out-of-time-ordered four-point functions, are also singular at the critical point, leading to interesting new critical exponents. The other model, with reduced ${\rm U}(n)$ symmetry, has a quantum critical point at strictly zero temperature and positive critical mass $m_*$. For $0<m<m_*$, it flows to a new gapless IR fixed point, for which the standard scale invariance is spontaneously broken by the appearance of distinct scaling dimensions $\Delta_+$ and $\Delta_-$ for the Euclidean two-point function when $t\rightarrow +\infty$ and $t\rightarrow -\infty$ respectively. We provide several detailed and pedagogical derivations, including rigorous proofs or simplified arguments for some results that were already known in the literature.

First-order topological quantum phase transition in a strongly correlated ladder

We report on the discovery of a quantum tri-critical point (QTP) separating a line of first-order topological quantum phase transitions from a continuous transition regime in a strongly correlated one-dimensional lattice system. Specifically, we study a fermionic four-leg ladder supporting a symmetry-protected topological phase in the presence of on-site interaction, which is driven towards a trivial gapped phase by a nearest-neighbor interaction. Based on DMRG simulations, we show that, as a function of the interaction strength, the phase transition between the topological and the trivial phase switches from being continuous to exhibiting a first-order character. Remarkably, the QTP as well as the first-order character of the topological transition in the strongly correlated regime are found to clearly manifest in simple local observables.

Critical black holes in a large charge limit

The extended thermodynamics of Reissner–Nordström charged black holes in D-dimensional anti-de Sitter spacetime has a phase structure in the (T, p) plane that includes a line of first-order phase transitions ending in a second-order transition point. For each D[Formula: see text][Formula: see text]4, properties of the critical black hole at that point are explored, motivated by the observation that in D[Formula: see text][Formula: see text]4 its neighborhood plays a core role in defining a very special class of heat engines that asymptote to Carnot efficiency in the large charge limit. This new limit provides a model of a novel low-temperature thermodynamic system. The double limit of approaching the horizon while sending the charge large at an appropriate rate yields a fully decoupled D-dimensional Rindler spacetime with zero cosmological constant.

Viscous effects on the dynamical evolution of QCD matter during the first-order confinement phase transition in heavy-ion collisions

We investigate viscous effects on the dynamical evolution of QCD matter during the first-order phase transition, which may happen in heavy-ion collisions. We first obtain the first-order phase transition line in the QCD phase diagram under the Gibbs condition by using the MIT bag model and the hadron resonance gas model for the equation of state of partons and hadrons. The viscous pressure, which corresponds to the friction in the energy balance, is then derived from the energy and net baryon number conservation during the phase transition. We find that the viscous pressure relates to the thermodynamic change of the two-phase state and thus affects the timescale of the phase transition. Numerical results are presented for demonstrations.

On the existence of thermodynamically stable rigid solids

Customarily, crystalline solids are defined to be rigid since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the metastable state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then used to obtain the equilibrium free energy as a function of this variable. Our results lead to a unique view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable when an external field, which penalizes particle rearrangements, is switched on. This produces a line of first-order phase transitions in the field-strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.

(H,Ti)-diagram of magnetic transformations induced by a pulsed magnetic field in antiferromagnetic LiCoPO4

A study of the differential magnetic susceptibility and electric polarization of an antiferromagnetic LiCoPO4 crystal in a pulsed magnetic field with an intensity of up to 290 kOe, directed along the antiferromagnetism vector of the spin-ordering main mode (Hǁb), at initial sample temperatures between 1.6 and 20.8 K. An adiabatic (H, Ti)-diagram of magnetic phase transitions is constructed. In addition to the three transitions that were discovered earlier at helium temperatures, higher temperatures revealed singularities that indicate the existence of a first-order phase transition line in the high-field phase II, which ends at a critical point. The coordinates of the critical point at which the lines of the phase transitions bordering the region of existence of high-field phase III converge with the line of the phase transitions from phase II to the saturated paramagnetic phase, are also determined.

An Ising model for metal-organic frameworks.

We present a three-dimensional Ising model where lines of equal spins are frozen such that they form an ordered framework structure. The frame spins impose an external field on the rest of the spins (active spins). We demonstrate that this "porous Ising model" can be seen as a minimal model for condensation transitions of gas molecules in metal-organic frameworks. Using Monte Carlo simulation techniques, we compare the phase behavior of a porous Ising model with that of a particle-based model for the condensation of methane (CH4) in the isoreticular metal-organic framework IRMOF-16. For both models, we find a line of first-order phase transitions that end in a critical point. We show that the critical behavior in both cases belongs to the 3D Ising universality class, in contrast to other phase transitions in confinement such as capillary condensation.

The ± J model for the mixed-spin 1/2 and 5/2 system

The ± J model is studied for the mixed spin-1/2 and 5/2 system on the Bethe lattice with the coordination numbers q=3,4 and 6 in terms of the exact recursion relations. The effects of varying the crystal field D and probability p are investigated on the phase diagrams of the model. The thermal variations of the order-parameters are also studied with the external magnetic field h is turned on and off. It is found that the model exhibits either second- or first-order phase transition lines on the (T, D) planes for given p values with 0 ≤ p ≤ 1. In addition, the phase diagrams on the (T, p) planes for given D show that two second-order phase transition lines combine with the tips of the same first-order phase transition line from above and below at two tricritical points. Our investigation has not revealed any compensation temperatures which may be caused by the large temperature differences between the magnetization curves belonging to spin-1/2 and 5/2.

Dynamic critical temperature in MnIIFeIII bimetallic oxalates

MnIIFeIII bimetallic oxalates are described by a spin-5/2 Blume–Capel (BC) model on a layered honeycomb structure. The effects of the interlayer coupling, the single-ion anisotropy and the oscillating magnetic field on the dynamic critical temperature of the compounds are studied by a effective-field method based on Glauber-type stochastic dynamic. Dynamic phase diagrams are presented in the DA∕J1–T∕J1 and T∕J1–h0∕J1 planes, and the first-order phase transition lines and the critical end point are found. Compensated magnetization regions have also been plotted and the compounds exhibit an uncompensated magnetization in the antiferromagnetic phase. In particular, a two-compensation-temperature phenomenon has also been observed in MnIIFeIII bimetallic oxalates.

Phase-field-crystal model for ordered crystals.

We describe a general method to model multicomponent ordered crystals using the phase-field-crystal (PFC) formalism. As a test case, a generic B2 compound is investigated. We are able to produce a line of either first-order or second-order order-disorder phase transitions, features that have not been incorporated in existing PFC approaches. Further, it is found that the only elastic constant for B2 that depends on ordering is C_{11}. This B2 model is then used to study antiphase boundaries (APBs). The APBs are shown to reproduce classical mean-field results. Dynamical simulations of ordering across small-angle grain boundaries predict that dislocation cores pin the evolution of APBs.

The Potts Model on a Bethe Lattice in an External Field

A solution for the Potts model with arbitrary number of states on a Bethe lattice in a nonzero external field has been obtained. A line of first-order phase transitions has been constructed in the temperature – external-field plane, terminating at the point of the second-order phase transition. The magnitude of the magnetization jump on the phase-transition lines has been found, as well as some of the critical exponents characterizing this phase transition.

Absence of the O17 Knight-shift changes across the first-order phase transition line in Sr2RuO4

We performed $^{17}$O nuclear magnetic resonance measurements on superconducting (SC) Sr$_2$RuO$_4$ under in-plane magnetic fields. We found that no new signal appears in the SC state and that the $^{17}$O Knight shifts obtained from the double-site measurements remain constant across the first-order phase-transition line, as well as across the second-order phase-transition line as already reported. The present results indicate that the SC spin susceptibility does not decrease in the high-field region, although a magnetization jump in the SC state was reported at low temperatures. Because the spin susceptibility is unchanged in the SC state in Sr$_2$RuO$_4$, we suggest that the first-order phase transition across the upper critical field should be interpreted as a depairing mechanism other than the conventional Pauli-paramagnetic effect.

Phase transitions in Thirring’s model

In his pioneering work on negative specific heat, Walter Thirring introduced a model that is solvable in the microcanonical ensemble. Here, we give a complete description of the phase-diagram of this model in both the microcanonical and the canonical ensemble, highlighting the main features of ensemble inequivalence. In both ensembles, we find a line of first-order phase transitions which ends in a critical point. However, neither the line nor the point have the same location in the phase-diagram of the two ensembles. We also show that the microcanonical and canonical critical points can be analytically related to each other using a Landau expansion of entropy and free energy, respectively, in analogy with what has been done in (Cohen and Mukamel 2012 J. Stat. Mech. P12017). Examples of systems with certain symmetries restricting the Landau expansion have been considered in this reference, while no such restrictions are present in Thirring’s model. This leads to a phase diagram that can be seen as a prototype for what happens in systems of particles with kinematic degrees of freedom dominated by long-range interactions.

The [formula omitted] model for the mixed-spin 1/2 and 3/2 Blume–Capel model

The effects of the bimodal bilinear exchange interaction, ±J model, are investigated for the mixed-spin 1/2 and 3/2 Blume–Capel (BC) model on the Bethe lattice (BL). The bilinear exchange interaction is either turned on ferrimagnetically (J>0) or turned off antiferrimagnetically (J<0) with probabilities p and 1−p for the nearest-neighbor sites on the BL. The phase diagrams of the model are obtained with the inclusion of the crystal field interactions on the sites of spin-3/2 for the coordination number, q=3,4 and 6, for given p values. It was found that the model gives either second- or first-order phase transition lines for each given value of p. The temperatures of these lines increase with the increasing values of q.

Quantum spin liquid and electric quadrupolar states of single crystal Tb2+xTi2-xO7+y

The ground states of the frustrated pyrochlore oxide Tb2+xTi2-xO7+y, sensitively depending on the small off-stoichiometry parameter x, have been studied by specific heat measurements using well characterized samples. Single crystal Tb2+xTi2-xO7+y boules grown by the standard floating zone technique are shown to exhibit concentration (x) gradient. This off-stoichiometry parameter is determined by precisely measuring the lattice constant of small samples cut from a crystal boule. Specific heat shows that the phase boundary of the electric quadrupolar state has a dome structure in the x-T phase diagram with the highest Tc ≃ 0.5 K at about x = 0.01. This phase diagram suggests that the putative U(1) quantum spin-liquid state of Tb2+xTi2-xO7+y exists in the range x < xc ≃ –0.0025, which is separated from the quadrupolar state via a first-order phase-transition line x = xc.

Phase Diagrams of the Semi-Infinite Blume-Capel Model with Mixed Spins (SA = 1 and SB = 3/2) by Migdal Kadanoff Renormalization Group

We study the mixed spin-1 and spin-3/2 Blume-Capel model under crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal-Kadanoff technique. As a function of the ratio R of bulk and surface interactions and the ratios R1 and R2 of bulk and surface crystals fields on the spin-1 and spin-3/2 respectively, we have determined various types of phase diagrams. Besides second- order transition lines, first-order phase transition lines terminating at tricritical points are obtained. We found that there existed nine main types of phase diagram showing a variety of phase transitions associated with the surface, including ordinary, extraordinary, surface and special phase transitions.

The van Hemmen model and effect of random crystalline anisotropy field

In this work, we have presented the generalized phase diagrams of the van Hemmen model for spin S=1 in the presence of an anisotropic term of random crystalline field. In order to study the critical behavior of the phase transitions, we employed a mean-field Curie–Weiss approach, which allows calculation of the free energy and the equations of state of the model. The phase diagrams obtained here displayed tricritical behavior, with second-order phase transition lines separated from the first-order phase transition lines by a tricritical point.

Phase diagrams of a finite superlattice with two disordered interfaces: Monte Carlo simulation

The phase diagrams and the magnetic properties of an Ising finite superlattice with two disordered interfaces are investigated using Monte Carlo simulations based on Metropolis algorithm. The superlattice consists of k unit cells, where the unit cell contains L layers of spin-1/2 (A atoms), L layers of spin-1 (B atoms), and a disordered interface, with two layers in between, which is characterized by a random arrangement of A and B atoms ApB1−pA1−pBp with a negative A–B coupling. The A–A and B–B exchange coupling are considered ferromagnetic. We have investigated the effects of the thickness of the film, the crystal field interactions and the surface exchanges coupling on the magnetic properties. The obtained results show that the number of compensation points and the number of first-order phase transition lines depend strongly on the thickness, the probability p and the exchange interactions in the surfaces.