Line Of First-order Phase Transitions Research Articles

Parasitic Small-Moment Antiferromagnetism and Nonlinear Coupling of Hidden Order and Antiferromagnetism inURu2Si2Observed by Larmor Diffraction

We report for the first time simultaneous microscopic measurements of the lattice constants, the distribution of the lattice constants, and the antiferromagnetic moment in high-purity URu(2)Si(2), combining Larmor and conventional neutron diffraction at low temperatures and pressures up to 18 kbar. Our data demonstrate quantitatively that the small moment in the hidden order (HO) of URu(2)Si(2) is purely parasitic. The excellent experimental conditions we achieve allow us to resolve that the transition line between HO and large-moment antiferromagnetism (LMAF), which stabilizes under pressure, is intrinsically first order and ends in a bicritical point. Therefore, the HO and LMAF must have different symmetry, which supports exotic scenarios of the HO such as orbital currents, helicity order, or multipolar order.

The second-order phase transition in the QCD phase diagram and a new approach for locating the critical point using RHIC low-energy-scan data

It is shown that the RHIC energy-scan experiments can serve as an effective tool for studying the system evolution along the first-order phase transition line passing the critical point, which is a second-order phase transition process. During this process the system structure changes while passing the critical point, and correspondingly, the transverse momentum of the final state particles gets an extra component. This phenomenon can provide useful information about the system structure in different phases and can serve as an effective signal for locating the critical point.

Interfacial and wetting properties of a binary point Yukawa fluid

We investigate the interfacial phase behavior of a binary fluid mixture composed of repulsive point Yukawa particles. Using a simple approximation for the Helmholtz free energy functional, which yields the random phase approximation for the pair direct correlation functions, we calculate the equilibrium fluid density profiles of the two species of particles adsorbed at a planar wall. We show that for a particular choice (repulsive exponential) of the wall potentials and the fluid pair-potential parameters, the Euler-Lagrange equations for the equilibrium fluid density profiles may be transformed into a single ordinary differential equation and the profiles obtained by a simple quadrature. For certain other choices of the fluid pair-potential parameters fluid-fluid phase separation of the bulk fluid is observed. We find that when such a mixture is exposed to a planar hard wall, the fluid exhibits complete wetting on the species 2 poor side of the binodal, i.e., we observe a thick film of fluid rich in species 2 adsorbed at the hard wall. The thickness of the wetting film grows logarithmically with the concentration difference between the fluid state point and the binodal and is proportional to the bulk correlation length of the intruding (wetting) fluid phase. However, for state points on the binodal that are further from the critical point, we find there is no thick wetting film. We determine the accompanying line of first-order (prewetting) surface phase transitions which separate a thin and thick adsorbed film. We show that for some other choices of repulsive wall potentials the prewetting line is still present, but its location and extent in the phase diagram is strongly dependent on the wall-fluid interaction parameters.

Phase diagram of a two-dimensional large- Q Potts model in an external field

We use a two-dimensional Wang–Landau sampling algorithm to map out the phase diagram of a Q-state Potts model with Q ⩽ 10 in an external field H that couples to one state. Finite-size scaling analyses show that for large Q the first-order phase transition point at H = 0 is in fact a triple point at which three first-order phase transition lines meet. One such line is restricted to H = 0 ; another line has H ⩽ 0 . The third line, which starts at the H = 0 triple point, ends at a critical point ( T c , H c ) which needs to be located in a two-dimensional parameter space. The critical field H c ( Q ) is positive and decreases with decreasing Q, which is in qualitative agreement with previous predictions.

Dissolved deconfinement: Phase structure of largeNgauge theories with fundamental matter

A class of large $N$ $U(N)$ gauge theories on a compact manifold ${S}^{3}\ifmmode\times\else\texttimes\fi{}\mathbb{R}$ (with possible inclusion of adjoint matter) is known to show first-order deconfinement transition at the deconfinement temperature. This includes the familiar example of pure $YM$ theory and $\mathcal{N}=4$ Supersymmetric Yang-Mills theory. Here we study the effect of introduction of ${N}_{f}$ fundamental matter fields in the phase diagram of the above mentioned gauge theories at small coupling and in the limit of large $N$ and finite ${N}_{f}/N$. We find some interesting features like the termination of the line of first-order deconfinement phase transition at a critical point as the ratio ${N}_{f}/N$ is increased and absence of deconfinement transition thereafter (there is only a smooth crossover). This result may have some implication for QCD, which unlike a pure gauge theory does not show a first-order deconfinement transition and only displays a smooth crossover at the transition temperature.

Uncovering the secrets of unusual phase diagrams: applications of two-dimensional Wang-Landau sampling

We use a two-dimensional Wang-Landau sampling algorithm to calculate the density of states for two discrete spin models and then extract their phase diagrams. The first system is an asymmetric Ising model on a triangular lattice with two- and three-body interactions in an external field. An accurate density of states allows us to locate the critical endpoint accurately in a two-dimensional parameter space. We observe a divergence of the spectator phase boundary and of the temperature derivative of the magnetization coexistence diameter at the critical endpoint in quantitative agreement with theoretical predictions. The second model is a Q-state Potts model in an external field H. We map the phase diagram of this model for Q > 8 and observe a first-order phase transition line that starts at the H = 0 phase transition point and ends at a critical point (Tc,Hc), which must be located in a two-dimensional parameter space. The critical field Hc(Q) is positive and increases with Q, in qualitative agreement with previous theoretical predictions.

Updating the phase diagram of the Gross–Neveu model in [formula omitted] dimensions

The method of optimized perturbation theory (OPT) is used to study the phase diagram of the massless Gross–Neveu model in 2+1 dimensions. In the temperature and chemical potential plane, our results give strong support to the existence of a tricritical point and line of first-order phase transition, previously only suspected to exist from extensive lattice Monte Carlo simulations. In addition of presenting these results we discuss how the OPT can be implemented in conjunction with the Landau expansion in order to determine all the relevant critical quantities.

The crystal field effects for the Ising bilayer system consisting of spin-3/2 and spin-1/2

A model consisting of two Bethe lattices each with a branching ratio of q Ising spins with one layer having spin-3/2 with nearest-neighbor (NN) interaction J1 and crystal field interaction Δ, and the other having spin-1/2 with NN interaction J2 is considered. The layer with spin-3/2 is laid over the top of the other with spin-1/2 and the two layers are tied together via an interaction between the vertically aligned spins denoted as J3. After obtaining the ground state (GS) phase diagrams on different possible planes depending on the given system parameters, the variations of the order-parameters and the free energy are investigated using the exact recursion relations in a pairwise approach to obtain the temperature dependent phase diagrams of the model by considering only the ferromagnetic ordering of the layers, i.e. J1>0 and J2>0, and ferromagnetic or antiferromagnetic ordering of the adjacent NN spins of the layers, J3>0 or J3>0, respectively. Besides the second-order phase transition lines with different kinds of behaviors, the first-order phase transition lines either ending at a tricritical point or at an isolated critical point are found. The model presents compensation temperatures when J2 of the lower layer can compete with J1 of the upper layer. The paramagnetic phase is also divided into two phases by studying the thermal behaviors of the quadrupolar moment for the layer with spin-3/2.

Mixed spin-2 and spin- Blume–Capel model

Abstract The influence of increasing the coordination number q on the phase diagrams of the mixed spin-2 and spin- 5 2 Blume–Capel Ising ferrimagnetic system with two crystal-field interactions, D A for spin-2 and D B for spin- 5 2 , is investigated on the Bethe lattice by using the exact recursion equations. The phase diagrams are obtained for the case with equal crystal field strengths when q = 3 , 4 and 6 on the ( k T / | J | , D / | J | ) planes and for the case with unequal crystal field strengths on the ( k T / | J | , D A / | J | ) and ( k T / | J | , D B / | J | ) planes for various values of D B / | J | and D A / | J | , respectively, for q = 4 and 6. Besides the second-order lines, the model presents three types of first-order phase transition lines; one of them ends on the compensation lines ( q = 3 ), the other one ends at a critical end point ( q = 4 ) and last one terminates at a tricritical point ( q = 6 ) for the case with equal crystal field strengths. In this case we have also observed up to four compensation temperatures when q = 6 . Besides the second-order, tricritical and compensation lines, the system presents two types of the first-order lines one of them ending at a tricritical point and the other one ending at an isolated point when unequal crystal field values are taken.

Theory of a two-dimensional superconductor with broken inversion symmetry

A detailed theory of a phase diagram of a two-dimensional surface superconductor in a parallel magnetic field is presented. A spin-orbital interaction of the Rashba type is known to produce at a high magnetic field $h$ (and in the absence of impurities) an inhomogeneous superconductive phase similar to the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) (Zh. Eksp. Teor. Fiz. 47, 1136 (1964) [Sov. Phys. JETP. 20, 762 (1965)]; Phys. Rev. 135, A550 (1964)) state with an order parameter $\ensuremath{\Delta}(\mathbf{r})\ensuremath{\propto}\mathrm{cos}(\mathbf{Q}\mathbf{r})$. We consider the case of a strong Rashba interaction with the spin-orbital splitting $\ensuremath{\alpha}m{v}_{F}$ (where $\ensuremath{\alpha}$ is the Rashba velocity) much larger than the superconductive gap $\ensuremath{\Delta}$, and show that at low temperatures $T\ensuremath{\leqslant}0.4{T}_{c0}$ the LOFF-type state is separated from the usual homogeneous state by a first-order phase transition line. At higher temperatures, a different inhomogeneous ``helical'' state with $\ensuremath{\Delta}(\mathbf{r})\ensuremath{\propto}\mathrm{exp}(i\mathbf{Q}\mathbf{r})$ intervenes between the uniform BCS state and the LOFF-like state at $g{\ensuremath{\mu}}_{B}h\ensuremath{\approx}1.5{T}_{c0}$. The modulation vector $Q$ in both phases is of the order of $g{\ensuremath{\mu}}_{B}h∕{v}_{F}$. The superfluid density ${n}_{s}^{yy}$ vanishes in the region around the second-order transition line between the BCS state and the helical state. Nonmagnetic impurities suppress both inhomogeneous states and eliminate them completely at ${T}_{c0}\ensuremath{\tau}\ensuremath{\leqslant}0.11$. However, once an account is made of the next-order term over the small parameter $\ensuremath{\alpha}∕{v}_{F}⪡1$, a relatively long wave helical modulation with $Q\ensuremath{\sim}g{\ensuremath{\mu}}_{B}h\ensuremath{\alpha}∕{v}_{F}^{2}$ is found to develop from the BCS state. This ground state carries zero current in the thermodynamic limit; however, under the cyclic boundary conditions a kind of ``spin-orbital Little-Parks oscillations'' [Phys. Rev. Lett. 9, 9 (1962)] is predicted. The long-wave helical modulation is stable with respect to disorder. In addition, we show that vortex defects with a continuous core may exist near the phase boundary between the helical and the LOFF-like states. In particular, in the LOFF-like state these defects may carry a half-integer flux.

Nonequilibrium Tricritical Point in a System with Long-Range Interactions

Systems with long-range interactions display a short-time relaxation towards quasistationary states whose lifetime increases with system size. With reference to the Hamiltonian mean field model, we here show that a maximum entropy principle, based on Lynden-Bell's pioneering idea of "violent relaxation," predicts the presence of out-of-equilibrium phase transitions separating the relaxation towards homogeneous (zero magnetization) or inhomogeneous (nonzero magnetization) quasistationary states. When varying the initial condition within a family of "water bags" with different initial magnetization and energy, first- and second-order phase transition lines are found that merge at an out-of-equilibrium tricritical point. Metastability is theoretically predicted and numerically checked around the first-order phase transition line.

Ground-state magnetic properties of the spin- [formula omitted] transverse Ising model

The ground-state phase diagrams and the magnetization curves of the spin- 3 2 transverse Ising model with longitudinal crystal field D are studied within the framework of mean-field theory (MFT) and effective-field theory (EFT), respectively. A simple calculation method of the internal energy is presented within the framework of EFT. In the ground-state phase diagram given by using EFT, the second-order phase transition line is divided into two segments by the first-order phase transition line: one starts from a critical end point and extends to D → - ∞ ; the other one starts from a tricritical point and extends to D → + ∞ , while it does not occur in MFT. Some interesting phenomena of the first-order phase transition from one ordered phase to another one ordered have been found.

State diagram of an antiferromagnet with a predominant Dzyaloshinskii interaction

A phase diagram in the variables Hz, Hy is constructed for an easy-axis tetragonal antiferromagnet with a predominant Dzyaloshinskii interaction. On this diagram the lines of second-order phase transitions between the canted phase and a phase in which the antiferromagnetic vector l is perpendicular to the easy axis begin and end at the fields of spin-flip transitions (i.e., at the exchange field). These lines of second-order phase transitions have the feature that each of them has two tricritical points, at which a transition occurs to a line of first-order phase transitions. The critical angle between the magnetic field direction and the basal plane, within which a first-order phase transition occurs, is determined. The value of this angle is temperature dependent. The position of the tricritical point on the Hz–Hy (or, equivalently, the Hz–Hy phase diagram is also temperature dependent.

Chiral transition ofN=4super Yang-Mills theory with flavor on a 3-sphere

We use the AdS/CFT correspondence to perform a numerical study of a phase transition in strongly-coupled large-${N}_{c}$ $\mathcal{N}=4$ Super-Yang-Mills theory on a 3-sphere coupled to a finite number ${N}_{f}$ of massive $\mathcal{N}=2$ hypermultiplets in the fundamental representation of the gauge group. The gravity dual system is a number ${N}_{f}$ of probe D7-branes embedded in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$. We draw the phase diagram for this theory in the plane of hypermultiplet mass versus temperature and identify for temperatures above the Hawking-Page deconfinement temperature a first-order phase transition line across which the chiral condensate jumps discontinuously.

Adiabatic computation: A toy model

We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter $s$ and the $\ensuremath{\alpha}$ parameter, which emulates many-variable constraints in the classical computational problem. The proposed model presents, in the $s\text{\ensuremath{-}}\ensuremath{\alpha}$ plane, a line of first-order quantum phase transition that ends at a second-order point. The relation between computation complexity and the occurrence of quantum phase transitions is discussed. We analyze the behavior of the ground and first excited states near the quantum phase transition, the gap, and the entanglement content of the ground state.

Phase transitions and multidomain states in magnetic nanostructures with competing anisotropies

The evolution of the magnetic states in nanostructures with competing surface and bulk anisotropies was studied under a variation in the applied magnetic field. For spatially uniform magnetic states, the energy functional reduces to the energy of a bulk magnet in which the effective anisotropy depends on the thickness of the ferromagnetic layer. This dependence results in spin reorientation as the nanolayer thickness varies. The lines of first-order phase transitions and the equilibrium parameters of multidomain structures and domains of competing phases were determined. The calculated magnetic phase diagrams are used to analyze magnetic states and to construct magnetization curves.

Phase diagram of antiferromagnetic cobalt fluoride

The H-T phase diagram of antiferromagnetic cobalt fluoride in an external magnetic field H perpendicular to the easy magnetization axis A is completed and used to construct a phase diagram in the variables Hz and Hy. In this diagram, the lines corresponding to second-order phase transitions (between an angular phase and a phase with antiferromagnetic vector I ⊥ A) begin and end in fields of a spin-flip transition (i.e., in an exchange field). A peculiarity of these lines of phase transitions is that each of them has two tricritical points at which this line of second-order phase transitions transforms into a line of first-order phase transitions. A critical angle between the direction of the external magnetic field and the basal plane within which the first-order phase transition takes place is determined.

Studies of phase transitions and quantum chaos relationships in extended Casten triangle of IBM-1

A precise solution of the classical energy functional E(N, η, χ; β) minimum problem with respect to deformation parameter β is obtained for the simplified Casten version of the standard interacting boson model (IBM-1) Hamiltonian. The first-order phase transition lines as well as the critical points of X(5), -X(5), and E(5) symmetries are considered. The dynamical criteria of quantum chaos—the basis state fragmentation width and the wave function entropy—are studied for the (η, χ) parameter space of the extended Casten triangle, and the possible relationships between these criteria and phase transition lines are discussed.

Role of isospin in the nuclear liquid–gas phase transition

We study the thermodynamics of asymmetric nuclear matter using a mean-field approximation with a Skyrme effective interaction, in order to establish its phase diagram and more particularly the influence of isospin on the order of the transition. A new statistical method is introduced to study the thermodynamics of a multifluid system, keeping only one density fixed, the others being replaced by their intensive conjugated variables. In this ensemble, phase coexistence reduces to a simple one-dimensional Maxwell construction. For a fixed temperature under a critical value, a coexistence line is obtained in the plane of neutron and proton chemical potentials. Along this line, the grand potential presents a discontinuous slope, showing that the transition is first order except at the two ending points where it becomes second order. This result is not in contradiction with the already reported occurrence of a continuous transformation when a constant proton fraction is imposed. Indeed, the proton fraction being an order parameter in asymmetric matter, the constraint can only be fulfilled by gradual phase mixing along the first-order phase-transition line, leading to a continuous pressure.

Mixed spin-3/2 and spin-5/2 Ising system on the Bethe lattice

In order to study the critical behaviors of the half-integer mixed spin-3/2 and spin-5/2 Blume–Capel Ising ferrimagnetic system, we have used the exact recursion relations on the Bethe lattice. The system was studied for the coordination numbers with q = 3 , 4, 5 and 6, and the obtained phase diagrams are illustrated on the ( k T c / | J | , D A / | J | ) plane for constant values of D B / | J | , the reduced crystal field of the sublattice with spin-5/2, and on the ( k T c / | J | , D B / | J | ) plane for constant values of D A / | J | , the reduced crystal field of the sublattice with spin-3/2, for q = 3 only, since the cases corresponding to q = 4 , 5 and 6 reproduce results similar to the case for q = 3 . In addition we have also presented the phase diagram with equal strengths of the crystal fields for q = 3 , 4, 5 and 6. Besides the second- and first-order phase transitions, the system also exhibits compensation temperatures for appropriate values of the crystal fields. In this mixed spin system while the second-order phase transition lines never cut the reduced crystal field axes as in the single spin type spin-3/2 and spin-5/2 Ising models separately, the first-order phase transition lines never connect to the second-order phase transition lines and they end at the critical points, therefore the system does not give any tricritical points. In addition to this, this mixed-spin model exhibits one or two compensation temperatures depending on the values of the crystal fields, as a result the compensation temperature lines show reentrant behavior.