First-order Transition Line Research Articles

Lattice polymers with two competing collapse interactions

We study a generalized model of self-avoiding trails, containing two different types of interaction (nearest-neighbour contacts and multiply visited sites), using computer simulations. This model contains various previously studied models as special cases. We find that the strong collapse transition induced by multiply-visited sites is a singular point in the phase diagram and corresponds to a higher order multi-critical point separating a line of weak second-order transitions from a line of first-order transitions.

Estimate of the phase transition line in the infinite-dimensional Hubbard model

We consider a Mott transition of the Hubbard model in infinite dimensions. The dynamical meanfield theory is employed in combination with a continuous-time quantum Monte Carlo (CTQMC) method for an accurate description at low temperatures. From the double occupancy and the energy density, which are directly measured from the CTQMC method, we construct the phase diagram. We pay particular attention to the construction of the first-order phase transition line (PTL) in the coexistence region of metallic and insulating phases. The resulting PTL is found to exhibit reasonable agreement with earlier finite-temperature results. We also show by a systematic inclusion of low-temperature data that the PTL, which is achieved independently of the previous zero-temperature results, approaches monotonically the transition point from earlier zerotemperature studies.

Yet another criticality of water

A phase behavior around the transition between ice VII and a plastic phase of water is investigated by molecular dynamics simulation and the subsequent analysis on the basis of Landau theory. The prior works have predicted that the phase transition between ice VII and plastic ice is a first-order transition on the ground of a weak hysteresis and so on. A rigorous survey in the present report, however, augments their prediction with new evidence that a first-order phase transition line gives way to a second-order one at higher pressures, where a tricritical point joins these phase boundaries together. Critical phenomena are also observed whereby, other than that associated with the hypothetical critical point in the deeply supercooled state, which could influence the physical properties in a wide range of temperatures and pressures. A new critical behavior is affirmed by the result that the scaling law holds at any pressure on the second-order phase transition line for which the critical exponents are estimated. We introduce an appropriate order parameter to obtain the Landau free energy functional and the change in the functional against temperature accounts for the phase behaviors. This also enables an estimate of the coexistence and the spinodal lines at pressures below the tricritical point, all of which compensate those obtained directly by molecular dynamics simulations. These results allow us to anticipate that the critical fluctuations may give us a clue for determining the phase boundary experimentally.

Phase diagrams of the spin-3/2 random transverse crystal field model

The mean-field approximation is used to calculate the phase diagrams of the spin-3/2 random transverse crystal field (RTCF) model. A bimodal distribution of the RTCF is employed in which one of the modes is in competition with the other mode whose strength is adjusted with a controllable parameter α. Thus, some sites in the lattice are under the effect of RTCF Dx with probability p and the rest of the sites are under the effect of αDx with 1 − p. The phase diagrams of the model are obtained on the RTCF-temperature planes by varying p on square lattices. Both second- and first-order phase transitions are displayed and thus tricritical points are also observed. The critical end points and end points for the first-order phase transition lines were also found.

The general-spin Blume–Capel model: A study of the multicritical behavior using effective-field theory

The general-spin Blume–Capel model is studied by using an effective-field theory with correlation. An expression for the free energy within the effective-field theory is proposed, and the complete phase diagram is constructed in the temperature and single-ion anisotropy plane. The first-order transition lines are obtained by Maxwell construction (comparison between free energies). Beyond first-order transitions at low temperatures, the results show second-order transitions and tricritical points, as well as a variety of double critical endpoints. The existence of the tricritical point and the number of critical endpoints strongly depend on the value of the spin.

Quantum spin-1 anisotropic ferromagnetic Heisenberg model in a crystal field: A variational approach

A variational approach based on Bogoliubov inequality for the free energy is employed in order to treat the quantum spin-1 anisotropic ferromagnetic Heisenberg model in the presence of a crystal field. Within the Bogoliubov scheme an improved pair approximation has been used. The temperature-dependent thermodynamic functions have been obtained and provide much better results than the previous simple mean-field scheme. In one dimension, which is still nonintegrable for quantum spin-1, we get the exact results in the classical limit, or near-exact results in the quantum case, for the free energy, magnetization, and quadrupole moment, as well for the transition temperature. In two and three dimensions the corresponding global phase diagrams have been obtained as a function of the parameters of the Hamiltonian. First-order transition lines, second-order transition lines, tricritical and tetracritical points, and critical endpoints have been located through the analysis of the minimum of the Helmholtz free energy and a Landau-like expansion in the approximated free energy. Only first-order quantum transitions have been found at zero temperature. Limiting cases, such as isotropic Heisenberg, Blume-Capel, and Ising models, have been analyzed and compared to previous results obtained from other analytical approaches as well as from Monte Carlo simulations.

Leading-order auxiliary-field theory of the Bose-Hubbard model

We discuss the phase diagram of the Bose-Hubbard (BH) model in the leading-order auxiliary field (LOAF) theory. LOAF is a conserving non-perturbative approximation that treats on equal footing the normal and anomalous density condensates. The mean-field solutions in LOAF correspond to first-order and second-order phase transition solutions with two critical temperatures corresponding to a vanishing Bose-Einstein condensate, $T_c$, and a vanishing diatom condensate, $T^\star$. The \emph{second-order} phase transition solution predicts the correct order of the transition in continuum Bose gases. For either solution, the superfluid state is tied to the presence of the diatom condensate related to the anomalous density in the system. In ultracold Bose atomic gases confined on a three-dimensional lattice, the critical temperature $T_c$ exhibits a quantum phase transition, where $T_c$ goes to zero at a finite coupling. The BH phase diagram in LOAF features a line of first-order transitions ending in a critical point beyond which the transition is second order while approaching the quantum phase transition. We identify a region where a diatom condensate is expected for temperatures higher than $T_c$ and less than $T_0$, the critical temperature of the non-interacting system. The LOAF phase diagram for the BH model compares qualitatively well with existing experimental data and results of \emph{ab initio} Monte Carlo simulations.

Liquid–liquid transition in supercooled water suggested by microsecond simulations

The putative liquid-liquid phase transition in supercooled water has been used to explain many anomalous behaviors of water. However, no direct experimental verification of such a phase transition has been accomplished, and theoretical studies from different simulations contradict each other. We investigated the putative liquid-liquid phase transition using the Water potential from Adaptive Force Matching for Ice and Liquid (WAIL). The simulation reveals a first-order phase transition in the supercooled regime with the critical point at ~207 K and 50 MPa. Normal water is high-density liquid (HDL). Low-density liquid (LDL) emerges at lower temperatures. The LDL phase has a density only slightly larger than that of the ice-Ih and shows more long-range order than HDL. However, the transformation from LDL to HDL is spontaneous across the first-order phase transition line, suggesting the LDL configuration is not poorly formed nanocrystalline ice. It has been demonstrated in the past that the WAIL potential provides reliable predictions of water properties such as melting temperature and temperature of maximum density. Compared with other simple water potentials, WAIL is not biased by fitting to experimental properties, and simulation with this potential reflects the prediction of a high-quality first-principle potential energy surface.

The magnetocaloric effect in itinerant antiferromagnetic materials

The Kondo lattice model is adopted to describe a variety of magnetic materials containing localized moments and conduction electrons. Within a mean-field approximation, we obtain the ground-state phase diagram including ferromagnetic (FM) and antiferromagnetic (AF) phases, as a function of the local FM exchange coupling JK and the conduction electron concentration n. The partial magnetizations are determined self-consistently as a function of temperature in presence of a magnetic field h. In the AF phase, we assume equivalent sublattices with independent magnetizations concomitant with charge ordering. The h–T phase diagram includes the homogeneous FM and AF phases, separated by a line of first-order metamagnetic transitions, and a PM phase at high temperatures. The magnetocaloric effect (MCE) is characterized by the isothermal entropy change ΔST, which can be evaluated by two alternative methods: (i) from the heat capacity or (ii) from the magnetization curves (via Maxwell relation). We verify the equivalence of the two methods, provided that the stable equilibrium states are taken into account. A metastable AF solution is allowed in a portion of the phase diagram. This feature may be associated to the presence of inhomogeneities in some compounds, which would lead to discrepancies between the two methods. The present approach describe the conversion from inverse to conventional MCE, as recently observed in some magnetocaloric materials with AF phases.

Mixed spin-[formula omitted] and spin-[formula omitted] Ising model with random crystal field distribution

The critical properties of the mixed-spin Ising model consisting of spin- 1/2 and 3/2 are investigated in the presence of a bimodal random crystal field by using the effective field theory with correlations. The thermal variations of magnetizations are studied in detail to obtain the phase diagrams. It was found that the model exhibits both second- and first-order phase transitions. The first-order phase transition lines always terminate at the isolated critical points. The model also yields one or two compensation temperatures for appropriate values of the random crystal fields.

Roberge-Weiss transition and ’t Hooft loops

Roberge and Weiss showed that for $SU(N)$ gauge theories, phase transitions occur in the presence of an imaginary quark chemical potential. We show that at asymptotically high temperature, where the phase transition is of first order, that even with dynamical quarks 't Hooft loops of arbitrary $Z(N)$ charge are well defined at the phase boundary. To leading order in weak coupling, the 't Hooft loop satisfies Casimir scaling in the pure glue theory, but not with quarks. Because the chemical potential is imaginary, typically the interaction measure is negative on one side of the phase transition. Using a matrix model to model the deconfining phase transition, we compute the phase diagram for heavy quarks, in the plane of temperature and imaginary chemical potential. In general we find intersecting lines of first order transitions. Using a modified Polyakov loop which is Roberge-Weiss symmetric, we suggest that the interface tension is related to the 't Hooft loop only at high temperature, where the imaginary part of this Polyakov loop, and not the real part, is discontinuous across the phase boundary.

Magnetization process and updated phase diagram of one-dimensional S=1 Ising model with single-ion anisotropy under magnetic field

By the infinite time-evolving block decimation (iTEBD) technique, the magnetization process in spin-1 Ising model with single-ion anisotropy under external field is investigated in the thermodynamic limit. An updated phase diagram is proposed, and the detailed magnetic structures of the phase diagram are uncovered. It must be noted that two interesting phases with same magnetization plateau (Mz=0) but different magnetic structures are distinguished. Furthermore, they are verified to be an ideal Néel phase and an ideal large-D phase respectively. In addition, a first-order quantum phase transition line between them is determined to be at D=1.

Mean field theory of effective spin models as a baryon fugacity expansion

The free energy of effective spin or "Polyakov line" models with a chemical potential, based on the U(N) group, does not depend on the chemical potential. In a mean field-inspired expansion, we show how the condition of unit determinant, taking U(N) to SU(N), reintroduces the chemical potential, and allows us to express the free energy, as a function of mean field variational parameters, in terms of an expansion in the baryon (rather than the quark) fugacity at each lattice site. We solve the SU(3) mean field equations numerically to determine the phase diagram and compute observables. We also calculate the first corrections to the leading order mean field results, and find that these can significantly shift the endpoint of a line of first order transitions. The problem of deriving an effective spin model from full QCD is discussed.

Coexistence and competition of nematic and gapped states in bilayer graphene

In bilayer graphene, the phase diagram in the plane of a strain-induced bare nematic term ${\mathcal{N}}_{0}$ and a top-bottom gates voltage imbalance ${U}_{0}$ is obtained by solving the gap equation in the random-phase approximation. At nonzero ${\mathcal{N}}_{0}$ and ${U}_{0}$, the phase diagram consists of two hybrid spin-valley symmetry-broken phases with both nontrivial nematic and mass-type order parameters. The corresponding phases are separated by a critical line of first- and second-order phase transitions at small and large values of ${\mathcal{N}}_{0}$, respectively. The existence of a critical end point where the line of first-order phase transitions terminates is predicted. For ${\mathcal{N}}_{0}=0$, a pure gapped state with a broken spin-valley symmetry is the ground state of the system. As ${\mathcal{N}}_{0}$ increases, the nematic order parameter increases, and the gap weakens in the hybrid state. For ${U}_{0}=0$, a quantum second-order phase transition from the hybrid state into a pure gapless nematic state occurs when the strain reaches a critical value. A nonzero ${U}_{0}$ suppresses the critical value of the strain. The relevance of these results to recent experiments is briefly discussed.

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

The spin-1 Blume–Capel model on a square lattice is studied by using an effective-field theory (EFT) with correlation. We propose an expression for the free energy within the EFT. The phase diagram is constructed in the temperature (T) and single-ion anisotropy amplitude (D) plane. The first-order transition line is obtained by Maxwell construction (comparison between free energies). Our results predict first-order transitions at low temperatures and large anisotropy strengths, which correspond in the phase diagram to the existence of a tricritical point (TCP). We compare our results with mean-field approximation (MFA), that show a qualitative correct behavior for the phase diagram.

Fate of the cluster state on the square lattice in a magnetic field

The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the presence of external magnetic fields by means of different types of high-order series expansions and variational techniques using infinite Projected Entangled Pair States (iPEPS). The phase diagram displays a first-order phase transition line ending in two critical end points. Furthermore, it contains a characteristic self-dual line in parameter space allowing many precise statements. The self-duality is shown to exist on any lattice topology.

Hairy black holes in massive gravity: Thermodynamics and phase structure

The thermodynamic properties of a static and spherically symmetric hairy black hole solution arising in massive gravity with spontaneous Lorentz breaking are investigated. The analysis is carried out by enclosing the black hole in a spherical cavity whose surface is maintained at a fixed temperature $T$. It turns out that the ensemble is well-defined only if the ``hair'' parameter $Q$ characterizing the solution is conserved. Under this condition we compute some relevant thermodynamic quantities, such as the thermal energy and entropy, and we study the stability and phase structure of the ensemble. In particular, for negative values of the hair parameter, the phase structure is isomorphic to the one of Reissner-Nordstrom black holes in the canonical ensemble. Moreover, the phase diagram in the plan $(Q,T)$ has a line of first-order phase transition that at a critical value of $Q$ terminates in a second-order phase transition. Below this line the dominant phase consists of small, cold black holes that are long-lived and may thus contribute much more to the energy density of the Universe than what is observationally allowed for radiating black holes.

First Order Metamagnetic Transition inHo2Ti2O7Observed by Vibrating Coil Magnetometry at Milli-Kelvin Temperatures

We report vibrating coil magnetometry of the spin-ice system Ho(2)Ti(2)O(7) down to ~0.04 K for magnetic fields up to 5 T applied parallel to the [111] axis. History-dependent behavior emerges below T(0)(*) ~ 0.6 K near zero magnetic field, in common with other spin-ice compounds. In large magnetic fields, we observe a magnetization plateau followed by a hysteretic metamagnetic transition. The temperature dependence of the coercive fields as well as the susceptibility calculated from the magnetization identify the metamagnetic transition as a line of first order transitions terminating in a critical end point at T(m)(*) 0.37 ~/= K, B(m) ~/= 1.5 T. The metamagnetic transition in Ho(2)Ti(2)O(7) is strongly reminiscent of that observed in Dy(2)Ti(2)O(7), suggestive of a general feature of the spin ices.

Inhomogeneous chiral symmetry breaking phases

We investigate inhomogeneous chiral symmetry breaking phases in the phase diagram of the two-flavor Nambu-Jona-Lasinio model, concentrating on phases with one-dimensional modulations. It is found that the first-order transition line in the phase diagram of homogeneous phases gets completely covered by an inhomogeneous phase which is bordered by second-order transition lines. The inhomogeneous phase turns out to be remarkably stable when vector interactions are included.

Phase diagram of the toric code model in a parallel magnetic field

Ground-state phase diagram of the toric code model in a parallel magnetic field has three distinct phases: topological, charge-condensed, and vortex-condensed states. To study it we consider an implicit local order parameter characterizing the transition between the topological and charge-condensed phases, and sample it using continuous-time Monte Carlo simulations. The corresponding second-order transition line is obtained by finite-size scaling analysis of this order parameter. Symmetry breaking between charges and vortices along the first-order transition line is also observed, and our numerical result shows that the end point of the first-order transition line is located at $h_x^{(c)}=h_z^{(c)}=0.418(2)$.