Second-order Phase Transition Lines Research Articles

Monte Carlo and mean-field studies on the magnetic properties of a hexagonal Ising nanowire with core-shell structure in the Blume–Emery–Griffiths model

The mean-field approximation based on the Gibbs-Bogoliubov inequality and Monte Carlo simulations based on the Metropolis method in the Blume–Emery–Griffiths model were used to successfully examine a hexagonal Ising nanowire with spin-1. It was found that the model displays fascinating phase diagrams in various planes of interest by using both methods. The investigation of magnetic hysteresis cycles also exhibits interesting properties. The model not only presents first- and second-order phase transition lines, but also the tricritical and isolated critical points, multi-compensation temperatures, and magnetic hysteresis behavior with one to eight cycles.

Critical and tricritical singularities from small-scale Monte Carlo simulations: the Blume–Capel model in two dimensions

We show that accurate insights into the critical properties of the Blume–Capel model at two dimensions can be deduced from Monte Carlo simulations, even for small system sizes, when one analyses the behaviour of the zeros of the partition function. The phase diagram of the model displays a line of second-order phase transitions ending at a tricritical point, then a line of first-order transitions. We concentrate on critical and tricritical properties and compare the accuracy achieved via standard finite-size scaling of thermodynamic quantities with that from the zeros analysis. This latter analysis showcases spectacular precision, even for systems as small as 64 spins. We also show that the zeros are very sensitive to subtle crossover effects.

Field-induced effects in the spin liquid candidate PbCuTe2O6

${\mathrm{PbCuTe}}_{2}{\mathrm{O}}_{6}$ is considered to be one of the rare candidate materials for a three-dimensional quantum spin liquid (QSL). This assessment was based on the results of various magnetic experiments, performed mainly on polycrystalline material. More recent measurements on single crystals revealed an even more exotic behavior, yielding ferroelectric order below ${T}_{\text{FE}}\ensuremath{\approx}1\phantom{\rule{0.28em}{0ex}}\text{K}$, accompanied by distinct lattice distortions, and a somewhat modified magnetic response which is still consistent with a QSL. Here we report on low-temperature measurements of various thermodynamic, magnetic, and dielectric properties of single-crystalline ${\mathrm{PbCuTe}}_{2}{\mathrm{O}}_{6}$ in magnetic fields $B\ensuremath{\le}14.5\phantom{\rule{0.28em}{0ex}}\text{T}$. The combination of these various probes allows us to construct a detailed $B\text{\ensuremath{-}}T$ phase diagram including a ferroelectric phase for $B\ensuremath{\le}8$ T and a $B$-induced magnetic phase at $B\ensuremath{\ge}11$ T. These phases are preceded by or coincide with a structural transition from a cubic high-temperature phase into a distorted noncubic low-temperature state. The phase diagram discloses a ferroelectric quantum critical point at ${B}_{c1}=7.9\phantom{\rule{0.28em}{0ex}}\text{T}$, where the second-order phase transition line associated with ferroelectric order is suppressed to zero. In addition, a magnetic quantum phase transition is revealed at ${B}_{c2}=11\phantom{\rule{0.28em}{0ex}}\text{T}$. The corresponding phase transition to a field-induced magnetic order at $B>{B}_{c2}$ is likely to be of first order. Field-induced lattice distortions, observed in the state at $T>1$ K and which are assigned to the effect of spin-orbit interaction of the ${\mathrm{Cu}}^{2+}$ ions, are considered as the key mechanism by which the magnetic field couples to the dielectric degrees of freedom in this material.

Critical and hysteresis behaviors for a hexagonal core-shell structure nanowire in the Blume–Emery–Griffiths model

The magnetic properties and hysteresis loops for the hexagonal Ising nanowire (HIN) with core–shell structure consisting of spin-32 are considered in the Blume–Emery–Griffiths (BEG) model by using the mean-field approximation (MFA) based on the Gibbs–Bogoliubov inequality for the free energy. The effects of various bilinear and biquadratic interaction parameters between the core, between the shell, and between the core and shell spins are considered for the phase diagrams of the model when temperature T=0 and T≠0 in addition to the crystal and external magnetic fields effects. The numerical calculations reveal that the model yields first- and second-order phase transition lines and tricritical points. In addition to the isolated critical and critical end-points, the model exhibits at most two compensation temperatures and interesting multiple hysteresis magnetic loops behaviors strongly dependent on the model parameters.

Random-anisotropy mixed-spin Ising on a triangular lattice

We have studied the mixed spin-1/2 and 1 Ising ferrimagnetic system with a random anisotropy on a triangular lattice with three interpenetrating sublattices A, B, and C. The spins on the sublattices are represented by σA (states ±1/2), σB (states ±1/2), and SC (states ±1, 0). We have performed Monte Carlo simulations to obtain the phase diagram temperature kBT/|J| versus the strength of the random anisotropy D/|J|. The phase boundary between two ferrimagnetic FR1 and FR2 phases at lower temperatures are always first-order for p < 0.25 and second-order phase transition between the FR1, FR2 and the paramagnetic P phases. On the other hand, for values of p ⪆ 0.5, the phase diagram presents only second-order phase transition lines.

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1 + 1)-dimensional Gross–Neveu model in the mean-field approximation* *The list of authors is sorted by (former) affiliations and surnames. All authors contributed in equal shares to this work. S Rechenberger initiated this project and produced preliminary results before leaving academia.

The phase diagram of the (1 + 1)-dimensional Gross–Neveu model is reanalyzed for (non-)zero chemical potential and (non-)zero temperature within the mean-field approximation. By investigating the momentum dependence of the bosonic two-point function, the well-known second-order phase transition from the symmetric phase to the so-called inhomogeneous phase is detected. In the latter phase the chiral condensate is periodically varying in space and translational invariance is broken. This work is a proof of concept study that confirms that it is possible to correctly localize second-order phase transition lines between phases without condensation and phases of spatially inhomogeneous condensation via a stability analysis of the homogeneous phase. To complement other works relying on this technique, the stability analysis is explained in detail and its limitations and successes are discussed in context of the Gross–Neveu model. Additionally, we present explicit results for the bosonic wave-function renormalization in the mean-field approximation, which is extracted analytically from the bosonic two-point function. We find regions—a so-called moat regime—where the wave function renormalization is negative accompanying the inhomogeneous phase as expected.

Thermodynamic theory of PbxSr1-xTiO3 solid solutions

The thermodynamic potential of the PbxSr1-xTiO3 solid solutions has been determined for the entire range of component concentrations. A phase diagram has been constructed, which contains: a critical point at which the line of second-order phase transitions passes into the line of first-order transitions between the cubic and tetragonal phases; a tricritical point at which the cubic, tetragonal, and rhombohedral phases converge; the multicritical point at which at low temperatures six phases converge along the lines of second-order transitions. The obtained T-x phase diagram of PbxSr1-xTiO3 shows the possibility of the existence of ferroelectric phases that were not previously observed in experiments.

Dynamics of a quantum phase transition in the Aubry-André-Harper model with p -wave superconductivity

We investigate the nonequilibrium dynamics of the one-dimension Aubry-Andr\'e-Harper model with $p$-wave superconductivity by changing the potential strength with slow and sudden quench. Firstly, we study the slow quench dynamics from the localized phase to the critical phase by linearly decreasing the potential strength $V$. The localization length is finite and its scaling obeys the Kibble-Zurek mechanism. The results show that the second-order phase transition line shares the same critical exponent $z\ensuremath{\nu}$, giving the correlation length $\ensuremath{\nu}=1$ and dynamical exponent $z=1.373\ifmmode\pm\else\textpm\fi{}0.023$, which are different from the Aubry-Andr\'e model. Secondly, we also study the sudden quench dynamics between three different phases: localized phase, critical phase, and extended phase. In the limit of $V=0$ and $V=\ensuremath{\infty}$, we analytically study the sudden quench dynamics via the Loschmidt echo. The results suggest that, if the initial state and the post-quench Hamiltonian are in different phases, the Loschmidt echo vanishes at some time intervals. Furthermore, we found that, if the initial value is in the critical phase, the direction of quenching is the same as one of the two limits mentioned before, and similar behaviors will occur.

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.

Ising chains with competing interactions in the presence of long-range couplings

In this paper we study an Ising spin chain with short-range competing interactions in the presence of long-range ferromagnetic interactions in the canonical ensemble. The simultaneous presence of the frustration induced by the short-range couplings together with their competition with the long-range term gives rise to a rich thermodynamic-phase diagram. We compare our results with the limit in which one of two local interactions is turned off, which was previously studied in the literature. Eight regions of parameters with qualitatively distinct properties are featured, with different first- and second-order phase transition lines and critical points.

λ Phase Transition in Horava Gravity

We present another example of superfluid black hole containing λ phase transition in Horava gravity. After studying the extended thermodynamics of general dimensional Horava-Lifshitz AdS black holes, it is found that only the one with spherical horizon in four and five dimensions has λ phase transition, which is a line of (continuous) second-order phase transitions and was famous in the discussion of superfluidity of liquid He4. The “superfluid” black hole phase and “normal” black hole phase are also distinguished. Particularly, six-dimensional Horava-Lifshitz AdS black holes exhibit infinitely many critical points in P-ν plane and the divergent points for specific heat, for which they only contain the “normal” black hole phase and the “superfluid” black hole phase disappears due to the physical temperature constraint; therefore there is no similar phase transition. In more than six dimensions, there is no P-ν critical behavior. After choosing the appropriate ordering field, we study the critical phenomena in different planes of thermodynamical phase space. We also calculate the critical exponents, which are the same as the van der Waals fluid.

Thermal properties of the mixed spin-1 and spin-3/2 Ising ferrimagnetic system with two different random single-ion anisotropies

In this work, we have performed Monte Carlo simulations to study a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on a square lattice with two different random single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins SA=1 in the sublattice A and SB=3∕2 in the sublattice B. The exchange interaction between the spins on the sublattices is antiferromagnetic (J<0). We used two random single-ion anisotropies, DiA and DjB, on the sublattices A and B, respectively. We have determined the phase diagram of the model in the critical temperature Tc versus strength of the random single-ion anisotropy D plane and we shown that it exhibits only second-order phase transition lines. We also shown that this system displays compensation temperatures for some cases of the random single-ion distribution.

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.

Magnetic phase transitions and the dynamic electric polarization in the LaMn2O5 compound

Possible phase transitions to the ferromagnetic phase in the LaMn2O3 compound have been studied in the framework of a phenomenological approach based on a symmetry analysis. The conditions that parameters of the thermodynamic potential must satisfy to realize a second-order transition have been found. The line of the first-order phase transitions in this system and the critical point of the second-order phase transition line have been determined. It was shown that a dynamic electric polarization can form in the antiferromagnetic phase.

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.

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.

Core–shell structured triangular Ising nanowire on the Bethe lattice

In this work, triangular type Ising nanowire is simulated on the Bethe lattice by using the core–shell structure consisting of Ising spins. A plaquette of spins, one at the center and the other three on the surface, present a nanoparticle which is then combined with other plaquettes, each with two nearest-neighbors. Then, they are allowed to interact via bilinear exchange interactions either ferromagnetically or antiferromagnetically. The thermal variations of magnetizations are studied to obtain the phase diagrams of the model. Because of the frustration of the system at low temperatures, only the second-order phase transition lines are presented. The magnetizations of the center and the surface spins compensate each other, i.e. the total magnetization goes to zero, for some values of the given system parameters.

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.

Frustrated mixed spin-1/2 and spin-1 Ising ferrimagnets on a triangular lattice.

Mixed spin-1/2 and spin-1 Ising ferrimagnets on a triangular lattice with sublattices A, B, and C are studied for two spin-value distributions (S(A),S(B),S(C))=(1/2,1/2,1) and (1/2,1,1) by Monte Carlo simulations. The nonbipartite character of the lattice induces geometrical frustration in both systems, which leads to the critical behavior rather different from their ferromagnetic counterparts. We confirm second-order phase transitions belonging to the standard Ising universality class occurring at higher temperatures, however, in both models these change at tricritical points (TCP) to first-order transitions at lower temperatures. In the model (1/2,1/2,1), TCP occurs on the boundary between paramagnetic and ferrimagnetic (±1/2,±1/2,∓1) phases. The boundary between two ferrimagnetic phases (±1/2,±1/2,∓1) and (±1/2,∓1/2,0) at lower temperatures is always first order and it is joined by a line of second-order phase transitions between the paramagnetic and the ferrimagnetic (±1/2,∓1/2,0) phases at a critical endpoint. The tricritical behavior is also confirmed in the model (1/2,1,1) on the boundary between the paramagnetic and ferrimagnetic (0,±1,∓1) phases.

Renormalization group flow in CDT

We perform a first investigation of the coupling constant flow of the nonperturbative lattice model of four-dimensional quantum gravity given in terms of causal dynamical triangulations (CDT). After explaining how standard concepts of lattice field theory can be adapted to the case of this background-independent theory, we define a notion of ‘lines of constant physics’ in coupling constant space in terms of certain semiclassical properties of the dynamically generated quantum universe. Determining flow lines with the help of Monte Carlo simulations, we find that the second-order phase transition line present in this theory can be interpreted as a UV phase transition line if we allow for an anisotropic scaling of space and time.