SOME THOUGHTS ON THE COSMOLOGICAL QCD PHASE TRANSITION

In the singlet Majoron model, we study cosmological phase transitions (PTs) and their resulting gravitational waves (GWs), in the two-field phase space, without freezing any of the field directions. We first calculate the effective potential, at one loop and at finite temperature, of the Standard Model Higgs doublet together with one extra Higgs singlet. We make use of the public available Python package ‘CosmoTransitions’ to simulate the two-dimensional (2D) cosmological PTs and evaluate the gravitational waves generated by first-order PTs. With the full 2D simulation, we are able not only to confirm the PTs’ properties previously discussed in the literature, but also we find new patterns, such as strong first-order PTs tunneling from a vacuum located on one axis to another vacuum located on the second axis. The two-field phase space analysis presents a richer panel of cosmological PT patterns compared to analysis with a single-field approximation. The PTGW amplitudes turn out to be out of the reach for the space-borne gravitational wave interferometers such as LISA, DECIGO, BBO, TAIJI and TianQin when constraints from colliders physics are taken into account.

The occurrence of first-order dimer phase transitions (PT) in quasi-one-dimensional lattice coupled anisotropic spin systems and one- and two-band Hubbard systems is studied. It is shown that a certain degree of exchange anisotropy of the $s=\frac{1}{2}$ Heisenberg chains is needed to obtain first-order PT. The first-order spin-dimer PT of the zig-zag chains in V${\mathrm{O}}_{2}$ is explained as a consequence of geometric constraints. The first-order metal-insulator PT observed in V${\mathrm{O}}_{2}$ is explained by means of the two-band Hubbard model. For the charge-transfer salts it is argued that a polarization instability is associated with the first-order spin-dimer PT which requires the isotropic Heisenberg model to be modified. The so far unexplained magnetic-excitation gap observed in uniformly stacked tetramethyl-$p$-phenylenediamine-tetracyanoquinodimethane (TMPD-TCNQ) crystals is attributed to a spin-polarization instability.

In many particle physics models, domain walls can form during the phase transition process after the breakdown of the discrete symmetry. Utilizing the ℤ3 symmetric complex singlet scalar extension of the Standard Model, we study the gravitational waves produced by the strongly first-order electroweak phase transition and the domain wall decay. The gravitational wave spectrum is of a typical two-peak shape. The high frequency peak corresponding to the strongly first-order electroweak phase transition is able to be probed by the future space-based interferometers, and the low frequency peak coming from the domain wall decay is far beyond the capability of the current Pulsar Timing Arrays, and future Square Kilometer Array.

To understand the mechanism of first-order magnetic phase transition in ordered FeRh thin films, the magnetic properties and first-order antiferromagnetic (AFM)–ferromagnetic (FM) phase transition behavior of single-crystal FeRh thin film are investigated in detail. The first-order magnetic phase transition is seen at a temperature of around 120 °C during heating and 145 °C cooling processes in perpendicular direction. The M–H loops measured isothermally amidst the AFM–FM transition regime show an opening at high magnetic field, which indicate a reversible AFM–FM transition induced by magnetic field. The clusters of the FM phase nucleate in the AFM matrix heterogeneously and vice versa during the first-order phase transition and the mechanism of nucleation and growth kinetics of the first-order magnetic phase transition in ordered FeRh thin film is quite similar to that of the crystallization of solids described by the Avrami model.

We calculate the gravitational wave spectrum generated by sound waves during a cosmological phase transition, incorporating several advancements beyond the current state-of-the-art. Rather than relying on the bag model or similar approximations, we derive the equation of state directly from the effective potential. This approach enables us to accurately determine the hydrodynamic quantities, which serve as initial conditions in a generalised hybrid simulation. This simulation tracks the fluid evolution after bubble collisions, leading to the generation of gravitational waves. Our work thus provides a self-consistent numerical calculation of gravitational waves for the real singlet extension of the standard model. Our computational method is adaptable to any particle physics model, offering a fast and reliable way to calculate gravitational waves generated by sound waves. With fewer approximations, our approach provides a robust foundation for precise gravitational wave calculations and allows for the exploration of model-independent features of gravitational waves from phase transitions.

view Abstract Citations (8) References (55) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and lambda -Transitions Christodoulou, Dimitris M. ; Kazanas, Demosthenes ; Shlosman, Isaac ; Tohline, Joel E. Abstract We use a free-energy minimization approach to describe in simple and clear physical terms the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Ginzburg-Landau theory of phase transitions. In this paper, we examine fourth-harmonic axisymmetric disturbances in Maclaurin spheroids and fourth-harmonic nonaxisymmetric disturbances in Jacobi ellipsoids. These two cases are very similar in the framework of phase transitions. It has been conjectured (Hachisu & Eriguchi 1983) that third-order phase transitions, manifested as smooth bifurcations in the angular momentum-rotation frequency plane, may occur on the Maclaurin sequence at the bifurcation point of the axisymmetric one-ring sequence and on the Jacobi sequence at the bifurcation point of the dumbbell-binary sequence. We show that these transitions are forbidden when viscosity maintains uniform rotation. The uniformly rotating one-ring/dumbbell equilibria close to each bifurcation point and their neighboring uniformly rotating nonequilibrium states have higher free energies than the Maclaurin/Jacobi equilibria of the same mass and angular momentum. These high-energy states act as free-energy barriers preventing the transition of spheroids/ellipsoids from their local minima to the free-energy minima that exist on the low rotation frequency branch of the one-ring/binary sequence. At a critical point, the two minima of the free-energy function are equal, signaling the appearance of a first-order phase transition. This transition can take place beyond the critical point only nonlinearly if the applied perturbations contribute enough energy to send the system over the top of the barrier (and if, in addition, viscosity maintains uniform rotation). In the angular momentum-rotation frequency plane, the one-ring and dumbbell-binary sequences have the shape of an "inverted S" and two corresponding turning points each. Because of this shape, the free-energy barrier disappears suddenly past the higher turning point, leaving the spheroid/ellipsoid on a saddle point but also causing a "catastrophe" by permitting a "secular" transition toward a one-ring/binary minimum energy state. This transition appears as a typical second-order phase transition, although there is no associated sequence bifurcating at the transition point (cf. Christodoulou et al. 1995a). Irrespective of whether a nonlinear first-order phase transition occurs between the critical point and the higher turning point or an apparent second-order phase transition occurs beyond the higher turning point, the result is fission (i.e., "spontaneous breaking" of the topology) of the original object on a secular timescale: the Maclaurin spheroid becomes a uniformly rotating axisymmetric torus, and the Jacobi ellipsoid becomes a binary. The presence of viscosity is crucial since angular momentum needs to be redistributed for uniform rotation to be maintained. We strongly suspect that the "secular catastrophe" is the dynamical analog of the notorious λ-transition of liquid 4He because it appears as a "second-order" phase transition with infinite "specific heat" at the point where the free-energy barrier disappears suddenly. This transition is not an elementary catastrophe. In contrast to this case, a "dynamical catastrophe" takes place from the bifurcation point to the lower branch of the Maclaurin toroid sequence because all conservation laws are automatically satisfied between the two equilibrium states. Furthermore, the free-energy barrier disappears gradually, and this transition is part of the elementary cusp catastrophe. This type of "λ-transition" is the dynamical analog of the Bose-Einstein condensation of an ideal Bose gas. The phase transitions of the dynamical systems are briefly discussed in relation to previous numerical simulations of the formation and evolution of protostellar systems. Some technical discussions concerning related results obtained from linear stability analyses, the breaking of topology, and the nonlinear theories of structural stability and catastrophic morphogenesis are included in an appendix. Publication: The Astrophysical Journal Pub Date: June 1995 DOI: 10.1086/175807 arXiv: arXiv:astro-ph/9504062 Bibcode: 1995ApJ...446..485C Keywords: GALAXIES: KINEMATICS AND DYNAMICS; GALAXIES: STRUCTURE; INSTABILITIES; STARS: FORMATION; STARS: ROTATION; Astrophysics E-Print: 34 pages, postscript, compressed,uuencoded. 7 figures available in postscript, compressed form by anonymous ftp from asta.pa.uky.edu (cd /shlosman/paper2 mget *.ps.Z). To appear in ApJ full text sources arXiv | ADS | Related Materials (3) Part 1: 1995ApJ...446..472C Part 3: 1995ApJ...446..500C Part 4: 1995ApJ...446..510C

Bismuth titanate Bi4Ti3O12 (BTO) is a member of the layered Aurivillius phase perovskite ferroelectrics and has a structural phase transition at Tc of 675 C. Below Tc, BTO shows ferroelectricity with a large spontaneous polarization (30 C/cm) parallel to the layered structure. BTO attracted much attention as candidate material for ferroelectric memories because of the fatigue-free nature of the BTO-based mixed crystal Bi4 xLaxTi3O12 (BLT-x). Although the space group of BTO at room temperature is determined to be B2cb ð1⁄4 Aba2 1⁄4 C2cbÞ (Z 1⁄4 4) only from the X-ray and neutron diffraction patterns, its space group has finally been concluded to be Pc (Z 1⁄4 2) with monoclinic symmetry, taking into account the existence of the small spontaneous polarization (4 C/cm) perpendicular to the layered structure. Here, Z is the number of the chemical formula in the conventional unit cell. Various physical properties of BTO, such as a soft mode behavior and domain wall structures, have been intensively investigated. The Landau theory of phase transition in BTO was presented by assuming the point group 4=mmm in the hightemperature phase, where the phase transition of BTO from the tetragonal (4=mmm) phase to the monoclinic (m) phase was named the triggered phase transition. The splitting of the triggered phase transition, that is the existence of the intermediate orthorhombic phase (B2cb), was observed in the mixed crystal systems in Bi4 xRxTi3O12 (R = La, Nd, Sm, and Gd). It was reported that the prototype structure of BTO shows the space group I4=mmm (Z 1⁄4 4). It is conjectured, however, that neither the orthorhombic (B2cb) nor the monoclinic (Pc) phase can be directly induced from the tetragonal (I4=mmm) phase, on the basis of the group theoretical consideration. Even the primitive unit cell size in I4=mmm and B2cb phases is different. Note that the proper ferroelectric phase transition from I4=mmm to B2cb is impossible, because the latter is not any subgroup of the former at the -point. On the other hand, it was reported, on the basis of experimental results, that the Curie–Weiss behavior of the dielectric constant in the high-temperature phase is observed in BTO, indicating the proper ferroelectric phase transition. This seems to be in contradiction. In order to solve the above contradiction, Rae et al. and Perez-Mato et al. assumed the Fmmm symmetry to be the parent phase, where Fmmm is a subgroup of I4=mmm. If the high-temperature parent phase above 675 C is indeed orthorhombic as they claim, however, the Landau theory so far proposed of the triggered phase transition in BTO, which is based on the assumption that it is tetragonal, may fail. Thus, the symmetry of the high-temperature parent phase seems to be of crucial importance. Under these circumstances, to clarify the structural phase transition at 675 C and the symmetry of the parent phase of BTO, we investigate the domain wall structure in the high-temperature phase and discuss its symmetry on the basis of the group theory. Single crystals of BTO were grown by the flux method from a Bi2O3–TiO2 system. For domain wall observation, some c-plate crystals with an area of about 5mm and thicknesses of about 10–50 m were selected among asgrown crystals as samples. The temperature dependence of the domain wall structure in the c-plate of the BTO crystal was observed using a polarizing microscope with a hightemperature sample stage (Linkam TS-1500), where the possible temperature range of this stage is from room temperature to a maximum of 1500 C. Figures 1(a) and 1(b) show photographs of the c-plate crystal in BTO under crossed-Nicols below and above Tc, respectively, where the sensitive plate was used in Fig. 1(b). In Fig. 1(a), the 90 domain wall structure is observed, while no domain wall structure appears in Fig. 1(b), indicating that the c-plate sample of BTO is optically isotropic. Thus, it was confirmed that the symmetry of the high-temperature phase is tetragonal. In our experiment, the phase front was also observed near Tc, indicating the first-order phase transition. 200 μm A P

The Ginzburg-Landau theory is developed to investigate coupling between a gas-liquid first-order phase transition (FOPT) and an orientational second-order phase transition (SOPT) in Langmuir monolayers. It is found that the coupled SOPT and FOPT takes place simultaneously if the uncoupled FOPT occurs prior to the SOPT with compression, and that in the opposite case, the coupling makes the FOPT take place at a lower pressure, but still behind the SOPT. Gas-liquid phase separation always leads to a decrease in the averaged order parameter of the orientational phase transition, which is qualitatively consistent with experimental data.

The freeze-in mechanism describes the out-of-equilibrium production of dark matter (DM) particles via feeble couplings or non-renormalisable interactions with large suppression scales. In the latter case, predictions suffer from a strong sensitivity to the initial conditions of the universe, such as the details of reheating. In this work, we investigate how this sensitivity is altered in the presence of a cosmological first-order phase transition. We show that freeze-in via non-renormalisable interactions is not always dominated by the highest temperatures of the Standard Model (SM) thermal bath, but instead may be governed by the period immediately after the phase transition, during which the decaying scalar field transfers its energy density to the SM radiation. We refer to this alternative production regime as DM phase-in. Using numerical and approximate analytical solutions of the relevant Boltzmann equations, we determine the conditions under which phase-in or conventional freeze-in production dominates the final DM abundance in terms of the type of interaction between the DM and SM particles, the amount of supercooling before and the evolution of the scalar field after the phase transition. In the phase-in regime, the DM abundance is correlated with the peak frequency of the gravitational wave signal associated with the phase transition, opening up new observational possibilities.

We discuss first-order electroweak phase transition in models with extended Higgs sectors for the case with relatively heavy additional scalar bosons. We first show that, by the combination of the sphaleron decoupling condition, perturbative unitarity and vacuum stability, mass upper bounds on additional scalar bosons can be obtained at the TeV scale even at the alignment limit where the lightest Higgs boson behaves exactly like the SM Higgs boson at tree level. We then discuss phenomenological impacts of the case with the additional scalar bosons with the mass near 1 TeV. Even when they are too heavy to be directly detected at current and future experiments at hadron colliders, the large deviation in the triple Higgs boson coupling can be a signature for first-order phase transition due to quantum effects of such heavy additional Higgs bosons. On the other hand, gravitational waves from the first-order phase transition are found to be weaker in this case as compared to that with lower masses of additional scalar bosons.

A Monte Carlo (MC) computer experiment for the analysis of first-order temperature-driven phase transitions in a system with one or many independently behaving order parameters is presented using the example of the three-dimensional (3D) Ashkin-Teller model, one of the important reference systems in statistical physics showing a rich and complex phase diagram. The properties of a number of quantities, such as magnetization, three types of cumulants, the internal energy, and its histogram, are exploited. The Lee and Kosterlitz concept proposed for strong first-order phase transitions in systems with one independent order parameter is significantly expanded to obtain results with comparable error bars in reasonable computation times at an arbitrary amount of latent heat. The proposed computer MC experiment uses parallel processing and both the Metropolis and recently formulated cluster algorithms. Arbitrarily weak to strong first-order phase transitions in the phase diagram region with ferromagnetic interactions are investigated and the latent heat associated with individual degrees of freedom is carefully computed. In the discussion of results, the behavior of our 3D system between that of the mean-field and that of the 2D one is bracketed and the role of the Potts point is clarified.

General formula for symmetry factors (S-factor) of Feynman diagrams containing fields with high spins is derived. We prove that symmetry factors of Feynman diagrams of well-known theories do not depend on spins of fields. In contributions to S-factors, self-conjugate fields and non self-conjugate fields play the same roles as real scalar fields and complex scalar fields, respectively. Thus, the formula of S-factors for scalar theories --- theories include only real and complex scalar fields --- works on all well-known theories of fields with high spins.Two interesting consequences deduced from our result are : (i) S-factors of all external connected diagrams consisting of only vertices with three different fields, e.g., spinor QED, are equal to unity; (ii) some diagrams with different topologies can contribute the same factor, leading to the result that the inverse S-factor for the total contribution is the sum of inverse S-factors, i.e., 1/S = \sum_i (1/S_i).

We have studied the first-order magnetic phase transition and related physical properties of MnFeP0.5As0.4Si0.1 by means of x-ray diffraction, magnetization, thermal expansion, and electrical resistance measurements. The compound crystallizes in the hexagonal structure with Fe2P-type. The temperature dependence of magnetization shows a first-order magnetic phase transition around 299 K. There is no crystallographic structural transition associated with the magnetic phase transition. The linear thermal expansion shows that this magnetic phase transition is accompanied by a negative volume change. The electrical resistance shows an anomalous behavior at the transition, which is probably caused by the change in c/a ratio.

Cosmological phase transitions can be a source of Stochastic Gravitational Wave (SGW) background. Apart from the dynamics of the phase transition, the characteristic frequency and the fractional energy density Ωgw of the SGW depends upon the temperature of the transition. In this article, we compute the SGW spectrum in the light of QCD equation of state provided by the lattice results. We find that the inclusion of trace anomaly from lattice QCD, enhances the SGW signal generated during QCD phase transition by ∼ 50% and the peak frequency of the QCD era SGW are shifted higher by ∼ 25% as compared to the earlier estimates without trace anomaly. This result is extremely significant for testing the phase transition dynamics near QCD epoch.

In recent years, the prospect of detecting gravitational waves sourced from a strongly first-order cosmological phase transition has emerged as one of the most exciting frontiers of gravitational wave astronomy. Cosmological phase transitions are an essential ingredient in the Standard Model of particle cosmology, and help explain the mechanism for creation of matter in the early Universe, provide insights into fundamental theories of physics, and shed light on the nature of dark matter. This underscores the significance of developing robust end-to-end tools for determining the resulting gravitational waves from these phase transitions. In this article we present PhaseTracer2, an improved version of the C++ software package PhaseTracer, designed for mapping cosmological phases and transitions in Standard Model extensions of multiple scalar fields. Building on the robust framework of its predecessor, PhaseTracer2 extends its capabilities by including new features crucial for a more comprehensive analysis of cosmological phase transitions. It can calculate more complex properties, such as the bounce action through the path deformation method or an interface with BubbleProfiler, thermodynamic parameters, and gravitational wave spectra. Its applicability has also been broadened via incorporating the dimensionally reduced effective potential for models obtained from DRalgo, as well as calculations in the MS¯ and OS-like renormalisation schemes. This modular, flexible, and practical upgrade retains the speed and stability of the original PhaseTracer, while significantly expanding its utility.