The absence of phase transition for the classical XY-model on Sierpiński pyramid with fractal dimension D=2

For the spin models with continuous symmetry on regular lattices and finite range of interactions, the lower critical dimension is d?=?2. In two dimensions the classical XY-model displays Berezinskii–Kosterlitz–Thouless (BKT) transition associated with unbinding of topological defects (vortices and antivortices). We perform a Monte Carlo study of the classical XY-model on Sierpiński pyramids (SPs) whose fractal dimension is D = log?4/log?2?=?2 and the average coordination number per site is ≈ 7. The specific heat does not depend on the system size which indicates the absence of a long-range order. From the dependence of the helicity modulus on the cluster size and on boundary conditions, we draw a conclusion that in the thermodynamic limit there is no BKT transition at any finite temperature. This conclusion is also supported by our results for linear magnetic susceptibility. The lack of finite temperature phase transition is presumably caused by the finite order of ramification of SP.     

Temperature and doping dependent flat-band superconductivity on the Lieb-lattice

We consider the superconducting properties of Lieb lattice, which produces a flat-band energy spectrum in the normal state under the strong electron–electron correlation. Firstly, we show the hole-doping dependent superconducting order amplitude with various electron–electron interaction strengths in the zero-temperature limit. Secondly, we obtain the superfluid weight and Berezinskii–Kosterlitz–Thouless(BKT) transition temperature with a lightly doping level. The large ratio between the gap-opening temperature and BKT transition temperature shows similar behavior to the pseudogap state in high-T_c superconductors. The BKT transition temperature versus doping level exhibits a dome-like shape in resemblance to the superconducting dome observed in the high-T_c superconductors. However, unlike the exponential dependence of T_c on the electron–electron interaction strength in the conventional high-T_c superconductors, the BKT transition temperature for a flat band system depends linearly on the electron–electron interaction strength. We also show the doping-dependent superconductivity on a lattice with the staggered hoping parameter in the end. Our predictions are amenable to verification in the ultracold atoms experiment and promote the understanding of the anomalous behavior of the superfluid weight in the high-T_c superconductors.     

Universality away from critical points in two-dimensional phase transitions

The p-state clock model in two dimensions is a system of discrete rotors with a quasiliquid phase in a region T14. We show that, for p>4 and above a temperature T(eu), all macroscopic thermal averages become identical to those of the continuous rotor (p=infinity). This collapse of thermodynamic observables creates a regime of extended universality in the phase diagram and an emergent symmetry, not present in the Hamiltonian. For p> or =8, the collapse starts in the quasiliquid phase and makes the transition at T2 identical to the Berezinskii-Kosterlitz-Thouless (BKT) transition of the continuous rotor. For p< or =6, the transition at T2 is below T(eu) and no longer a BKT transition. The results generate a range of experimental predictions, such as the motion of magnetic domain walls, and limits on macroscopic distinguishability of different microscopic interactions.     

BKT phase transition in a 2D system with long-range dipole-dipole interaction

We consider phase transitions in 2D XY-like systems with long-range dipole-dipole interactions and demonstrate that BKT-type phase transition always occurs separating the ordered (ferroelectric) and the disordered (paraelectric) phases. The low-temperature phase corresponds to a thermal state with bound vortex-antivortex pairs characterized by linear attraction at large distances. Using the Maier-Schwabl topological charge model, we show that bound vortex pairs polarize and screen the vortex-antivortex interaction, leaving only the logarithmic attraction at sufficiently large separations between the vortices. At higher temperatures the pairs dissociate and the phase transition similar to BKT occurs, though at a larger temperature than in a system without the dipole-dipole interaction.     

Critical Properties of a Generalized Planar Rotator Model

The critical properties of the planar rotator model with chiral Dzyaloshinsky-Moriya interaction are analyzed using a hybrid Monte Carlo method. Simulations on different lattices conform an observation that there is an XY-like Berezinskii-Kosterlitz-Thouless (BKT) phase transition in this model. The ground state and some thermodynamics properties are also discussed.     

A scheme to observe universal breathing mode and Berezinskii–Kosterlitz–Thouless phase transition in a two-dimensional photon gas

A system of two-dimensional photon gas has recently been realized experimentally. We show that this setup can be used to observe a universal breathing mode of photon gas and a modification in the experimental setup would open up a possibility of observing the Berezinskii–Kosterlitz–Thouless (BKT) phase transition in such a system. Furthermore, the universal jump in the superfluid density of light in the output channel can be used as an unambiguous signature for the experimental verification of the BKT transition.     

Chiral symmetry breaking and pion properties at finite temperatures

Spontaneous and explicit chiral symmetry breaking is analyzed in Coulomb gauge QCD at finite temperatures, using an instantaneous approximation for the quark interaction and incorporating confinement through a running coupling constant. The thermodynamics of the quarks is treated approximatively by assuming that the momentum-dependent constituent quark mass sets the scale for thermodynamic fluctuations of colour singlet excitations. We investigate the class of a temperature independent and a temperature dependent interaction between quarks. In the chiral limit both temperature independent and a smooth temperature dependent interaction yields a second order chiral phase transition with critical exponents close to the values for a BCS super-conductor. For explicit chiral symmetry breaking we find a nearly constant pion mass below the transition temperature, but a strongly overdamped mode above. For a first order deconfining transition in the gluonic sector also the quark sector shows a first order chiral phase transition. The relevance of our results for relativistic heavy ion collisions is briefly discussed.     

Topological phase transitions in the theory of partitions of integers

In the paper, the problem of partitioning a natural number into summands is considered in connection with the BKT (Berezinskii–Kosterlitz–Thouless) phase transition and its two critical points. As examples, the passage from superfluid state to normal state and from a cell-like vortical state to turbulent state are considered.     

Phase diagram of the D3/D5 system in a magnetic field and a BKT transition

We study the full temperature and chemical potential dependence of the D3/D5 2+1$2+1$-dimensional theory in the presence of a magnetic field. The theory displays separate transitions associated with chiral symmetry breaking and melting of the bound states. We display the phase diagram which has areas with first and second order transitions meeting at two critical points similar to that of the D3/D7 system. In addition there is the recently reported BKT transition at zero temperature leading to distinct structure at low temperatures.     

Superinsulator–superconductor duality in two dimensions

For nearly a half century the dominant orthodoxy has been that the only effect of the Cooper pairing is the state with zero resistivity at finite temperatures, superconductivity. In this work we demonstrate that by the symmetry of the Heisenberg uncertainty principle relating the amplitude and phase of the superconducting order parameter, Cooper pairing can generate the dual state with zero conductivity in the finite temperature range, superinsulation. We show that this duality realizes in the planar Josephson junction arrays (JJA) via the duality between the Berezinskii–Kosterlitz–Thouless (BKT) transition in the vortex–antivortex plasma, resulting in phase-coherent superconductivity below the transition temperature, and the charge-BKT transition occurring in the insulating state of JJA and marking formation of the low-temperature charge-BKT state, superinsulation. We find that in disordered superconducting films that are on the brink of superconductor–insulator transition the Coulomb forces between the charges acquire two-dimensional character, i.e. the corresponding interaction energy depends logarithmically upon charge separation, bringing the same vortex-charge-BKT transition duality, and realization of superinsulation in disordered films as the low-temperature charge-BKT state. Finally, we discuss possible applications and utilizations of superconductivity–superinsulation duality.     

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.     

Josephson vortex lattice melting in Bi-2212 probed by commensurate oscillations of Josephson flux-flow

We studied the commensurate semifluxon oscillations of Josephson flux-flow in Bi-2212 stacked structures near T_c as a probe of melting of a Josephson vortex lattice. We found that oscillations exist above 0.5 T. The amplitude of the oscillations is found to decrease gradually with the temperature and to turn to zero without any jump at T = T₀ (3.5 K below the resistive transition temperature T_c), thus, indicating a phase transition of the second order. This characteristic temperature T₀ is identified as the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, T_BKT, in the elementary superconducting layers of Bi-2212 at zero magnetic field. On the basis of these facts, we infer that melting of a triangular Josephson vortex lattice occurs via the BKT phase with formation of characteristic flux loops containing pancake vortices and antivortices. The B-T phase diagram of the BKT phase found from our experiment is consistent with theoretical predictions.     

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.     

Berezinsky-Kosterlitz-Thouless transition in phase fluctuating superconductors with inhomogeneous Gaussian distributed couplings

Within the framework of phase fluctuation picture for the pseudogap state of cuprate superconductors, we study the effects of both spatial inhomogeneity of coupling strength and thermal phase fluctuations on the superconducting transition temperature. Such a Berezinsky-Kosterlitz-Thouless (BKT) transition is characterized by a two-dimensional (2D) classical XY model, in which the bond coupling is assumed to be roughly proportional to the superconducting bond order parameter. In recent STM experiments with lattice-tracking spectroscopy technique, a Gaussian-like spatially distributed pairing strength is observed. Our Monte Carlo simulations using Wolff cluster update on such 2D classical XY model, in which the bond coupling obeys a similar spatial Gaussian distribution, indicate that the enhancement of the variance of Gaussian distribution may suppress the BKT transition temperature. In addition, we calculate the related physical quantities, including the spin stiffness, free energy, specific heat, magnetization and magnetic susceptibility, by changing the inhomogeneity variance.     

Theory for Difference Between Photoinduced Phase and Thermally Excited Phase

A possible difference between the photoinduced phase and the thermally excited one is studied by using a two-dimensional extended Peierls-Hubbard model, which includes a strong electron-phonon coupling and a on-site interelectron repulsion, as well as an anharmonic lattice potential. Because of this anharmonicity, the system undergoes a first order phase transition from an insulating CDW state to a metallic one at a high temperature. Although some sign of an SDW order is expected to appear due to this repulsion, it is always hidden in any equilibrium phase of the present system. In fact, it is hidden, not only in the CDW ground state, but also in this metallic one, since the high temperature itself destroys the SDW order, far before the CDW-metal transition occurs, while a photo-excitation at low enough temperature is shown to generate a local metastable SDW domain. Therefore, to observe the presence of such Coulomb interaction and the resultant broken symmetry, a nonequilibrium photoinduced phase is shown to be most straightforward. Thus, the photoinduce phase transition can make an interaction appear as a broken symmetry only in this phase, even though this interaction is almost completely hidden in all the equilibrium phases from low temperature to high ones.     

Mean field at finite temperature and symmetry breaking

For an infinite system of nucleons interacting through a central spin-isospin schematic force we discuss how the Hartree-Fock theory at finite temperature T yields back, in the T=0 limit, the standard zero-temperature Feynman theory when there is no symmetry breaking. The attention is focused on the mechanism of cancellation of the higher order Hartree-Fock diagrams and on the dependence of this cancellation upon the range of the interaction. When a symmetry breaking takes place it turns out that more iterations are required to reach the self-consistent Hartree-Fock solution, because the cancellation of the Hartree-Fock diagrams of order higher than one no longer occurs. We explore in particular the case of an explicit symmetry breaking induced by a constant, uniform magnetic field B acting on a system of neutrons. Here we compare calculations performed using either the single-particle Matsubara propagator or the zero-temperature polarization propagator, discussing under which perturbative scheme they lead to identical results (if B is not too large). We finally address the issue of the spontaneous symmetry breaking for a system of neutrons using the technique of the anomalous propagator: in this framework we recover the Stoner equation and the critical values of the interaction corresponding to a transition to a ferromagnetic phase.     

Phase structure of two-flavor QCD at finite chemical potential

We study the phase diagram of two-flavor QCD at imaginary chemical potentials in the chiral limit. To this end we compute order parameters for chiral symmetry breaking and quark confinement. The interrelation of quark confinement and chiral symmetry breaking is analyzed with a new order parameter for the confinement phase transition. We show that it is directly related to both the quark density as well as the Polyakov loop expectation value. Our analytical and numerical results suggest a close relation between the chiral and the confinement phase transition.     

Effects of isospin and momentum dependent interactions on liquid–gas phase transition in hot asymmetric nuclear matter

The liquid–gas phase transition in hot neutron-rich nuclear matter is investigated within a self-consistent thermal model using an isospin and momentum dependent interaction (MDI) constrained by the isospin diffusion data in heavy-ion collisions, a momentum-independent interaction (MID), and an isoscalar momentum-dependent interaction (eMDYI). The boundary of the phase-coexistence region is shown to be sensitive to the density dependence of the nuclear symmetry energy with a softer symmetry energy giving a higher critical pressure and a larger area of phase-coexistence region. Compared with the momentum-independent MID interaction, the isospin and momentum-dependent MDI interaction is found to increase the critical pressure and enlarge the area of phase-coexistence region. For the isoscalar momentum-dependent eMDYI interaction, a limiting pressure above which the liquid–gas phase transition cannot take place has been found and it is shown to be sensitive to the stiffness of the symmetry energy.     

Phase transition over the gauge group center and quark confinement in QCD

A lattice gauge model with the phase transition corresponding to spontaneous breakdown of the group center symmetry is considered. The possible continuum limit in a phase with permanently confined quarks is discussed.