Phase Transition Of Kosterlitz-Thouless Type Research Articles

Renormalization of the bilocal sine-Gordon model

The functional renormalization group treatment is presented for the two-dimensional sine-Gordon model including a bilocal term in the potential, which contributes to the flow at the tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, since it can recover the Kosterlitz–Thouless type phase transition. The flows can also reveal the connection between the sine-Gordon and the noninteracting Thirring models at a special value of the wave number parameter.

Thermal fluctuations in a system of microcavity exciton‐polariton condensations

AbstractThe exciton‐polariton condensation scenario in a microcavity matter–light system at finite temperature is investigated in the framework of the unrestricted Hartree–Fock approximation applying the two‐dimensional exciton‐polariton model. Treating electron–hole Coulomb interaction and matter–light coupling effects on an equal footing, we analyze the temperature influence on the excitonic and photonic order parameters. In the thermal equilibrium limit, the Kosterlitz–Thouless type phase transition of the exciton‐polariton condensation has been found. Depending on detuning and excitation density one finds that the system either favors the photonic or excitonic condensate. The effect of temperature on a crossover from a BCS‐excitonic to a BEC‐polaritonic condensed state then is discussed.

Universality for Moving Stripes: A Hydrodynamic Theory of Polar Active Smectics

We present a theory of moving stripes ("polar active smectics"), both with and without number conservation. The latter is described by a compact anisotropic Kardar-Parisi-Zhang equation, which implies smectic order is quasilong ranged in d=2 and long ranged in d=3. In d=2 the smectic disorders via a Kosterlitz-Thouless transition, which can be driven by either increasing the noise or varying certain nonlinearities. For the number-conserving case, giant number fluctuations are greatly suppressed by the smectic order, which is long ranged in d=3. Nonlinear effects become important in d=2.

Degeneracy induced scaling of the correlation length for periodic models

The broken symmetric phase of scalar models exhibits an infrared fixed point which is induced by the degenerate effective potential. The definition of the correlation length in the infrared regime enables us to determine the type of the phase transition in the model. It is shown that the massive sine-Gordon model exhibits a continuous, while the layered sine-Gordon model has an infinite order Kosterlitz–Thouless type phase transition.

Close packing density and fracture strength of adsorbed polydisperse particle layers

The close packing density of log-normal and bimodal distributed, surface-adsorbed particles or discs in 2D is studied by numerical simulation. For small spread in particle size, the system orders in a polycrystalline structure of hexagonal domains. The domain size and the packing density both decrease as the spread in particle size is increased up to 10.5 ± 0.5%. From this point onwards the system becomes amorphous, and the close packing density increases again with spread in particle size. We argue that the polycrystalline and amorphous regions are separated by a Kosterlitz–Thouless-type phase transition. In the amorphous region we find the close packing density to vary proportional to the logarithm of the friction factor, or cooling rate. We also studied the fracture behaviour of surface layers of sintered particles. Fracture strength increases with spread in particle size, but the brittleness of the layers shows a minimum at the polycrystalline–amorphous transition. We further show that mixing distributions of big and small particles generally leads to weaker and more brittle layers, even though the close packing density is higher than for either of the particle types. We point out applications to foam stability by the Pickering mechanism.

Electrostatic screening and experimental evidence of a topological phase transition in a bulk quantum Hall liquid

The electrostatic screening of a medium disordered quantum Hall liquid was investigated using an electric field penetration (EFP) technique. At sufficiently low temperatures and at magnetic fields corresponding to the integral quantum Hall regime with even filling factors, two topologically different phases of the bulk electron liquid have been identified. By means of elementary analysis of experimental data it has further been shown that the transition between these phases reveals features typical of a Kosterlitz–Thouless type phase transition. Finally, the validity of the presented physical picture has been supported by means of numerical simulations of local filling factor topography.

EVOLUTION AND DESTRUCTION OF THE KONDO EFFECT IN A CAPACITIVELY COUPLED DOUBLE DOT SYSTEM

We consider the simplest example of a double quantum dot system: two equivalent, capacitively coupled single-level dots, each coupled to its own lead. Focussing on a regime of two electrons on the double dot, a rich range of behaviour is found on increasing the interdot coupling: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom; followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi liquid 'charge-ordered' phase with finite residual entropy and anomalous transport properties. The numerical renormalization group method, coupled with simple physical arguments, is employed to obtain a detailed understanding of the problem.

Quantum Phase Transition in Capacitively Coupled Double Quantum Dots

We investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling, a rich range of behavior is uncovered: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom, followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi-liquid "charge-ordered" phase with finite residual entropy and anomalous transport properties. Physical arguments and numerical renormalization group methods are employed to obtain a detailed understanding of the problem.

Study of the fully frustrated clock model using the Wang–Landau algorithm

Monte Carlo simulations using the newly proposed Wang-Landau algorithm together with the broad histogram relation are performed to study the antiferromagnetic six-state clock model on the triangular lattice, which is fully frustrated. We confirm the existence of the magnetic ordering belonging to the Kosterlitz-Thouless (KT) type phase transition followed by the chiral ordering which occurs at slightly higher temperature. We also observe the lower temperature phase transition of KT type due to the discrete symmetry of the clock model. By using finite-size scaling analysis, the higher KT temperature $T_2$ and the chiral critical temperature $T_c$ are respectively estimated as $T_2=0.5154(8)$ and $T_c=0.5194(4)$. The results are in favor of the double transition scenario. The lower KT temperature is estimated as $T_1=0.496(2)$. Two decay exponents of KT transitions corresponding to higher and lower temperatures are respectively estimated as $\eta_2=0.25(1)$ and $\eta_1=0.13(1)$, which suggests that the exponents associated with the KT transitions are universal even for the frustrated model.

Polymorphic phase transitions in systems evolving in a two-dimensional discrete space.

Polymorphic phase transitions in systems evolving in a two-dimensional discrete space have been studied. The driving force of the transitions appears to be a difference between two main energetic contributions: one, related to the thermal activation of the process, and another, being of quantum nature. The former (high temperature limit) is naturally assigned to the expansion (melting) part of the transition, while the latter (low temperature limit) has much in common with the contraction (solidification) part. Between the two main physical states distinguished, there exists a certain state, corresponding to a discontinuity point (pole) in the morphological phase diagram, represented by the well-known Bose-Einstein (Planck) formula, in which the system blows up. This point is related to an expected situation in which the contour of the object under investigation stands for the Brownian or purely diffusional path, with the fractal dimension dw=2, and the situation can be interpreted as some emergence of an intermediate "tetratic" phase. This, in turn, recalls a certain analogy to the equilibrium (order-disorder) phase transition of Kosterlitz-Thouless type, characteristic of, e.g., rough vs rigid interfaces in a two-dimensional space, with some disappearance of interface correlation length at dw=2. Otherwise, the contours of the objects are equivalent to fractional Brownian paths either in superlinear or "turbulent" (dw<2; the expansion case), or sublinear, viz., anomalously slow (dw>2; the contraction case) regimes, respectively. It is hoped that the description offered will serve to reflect properly the main subtleties of the dynamics of the polymorphic transitions in complex "soft-matter" systems, like formation of lipid mesomorphs or diffusional patterns, with nonzero line tension effect.

Application of the Cluster Variation Method to the Ferromagnetic Six-State Clock Model on the Triangular Lattice and Its CAM Analysis

The cluster variation method is applied to the ferromagnetic six-state clock model on the triangular lattice up to the hexagonal cluster approximation. The Kosterlitz-Thouless type phase transition of the model is studied by using the coherent anomaly method (CAM).

Numerical Solution of 2 + 1 Dimensional Wave Equation with Charge and Flux

2+1 dimensional Schrodinger equations and Dirac equations are solved numerically when there is Aharonov-Bohm like external potential. Energy of ground state shows singular behavior as the function of coupling parameters. We investigate further the feature of the gas of composite anyon pairs with opposite sign of charge and flux. Energy of the system has discontinuity when flux is changed. On the basis of WKB approximation, we show the flux-dependence of the specific heat C and phase transition of Kosterlitz-Thouless type when each particle has flux. Van der Waals' force of this system shows order changing at a particular value of flux

Thermodynamics of handles

We consider spin 1 2 free fermions on hyperelliptic Riemann surfaces including the infinite genus ones to study the configuration of the surfaces. The grand partition function of this system on the universal moduli space is defined using the branch point operator method. By taking a Coulomb gas analogy we observe a Kosterlitz-Thouless type phase transition on the universal moduli space which can be interpreted as the fusion and the condensation of handles. As a result, the notion of genus is lost. This is completely an analogy of a “thermodynamic” effect beyond the mathematical structure of the theory. Some remarks on the implication on string theories are also made.

Magnetic phase transitions in CoCl2-graphite intercalation compounds

Magnetic intercalation compounds of stage 1, 2, and 3 CoCl2 -GIC have been successfully prepared and characterized by x-ray diffraction, Raman scattering, and transmission electron microscopy. The temperature dependence of the magnetic susceptibility of these samples show two superposed peaks. The difference in the magnetic field dependence of these two peaks indicates that at least two magnetic states are present. The higher temperature peak is identified with a Kosterlitz-Thouless type phase transition for finite size systems. Above the upper transition temperature (Tcu ), the magnetic system consists of unbound vortices and below Tcu the vortices are bound. For low stage samples (stage ≤ 2), the lower temperature peak is identified with a transition showing crossover from two dimensional to three dimensional behavior. Below the lower transition temperature (Tcl ), the system is in a phase showing long range magnetic order in which the spins are coupled ferromagnetically in-plane and antiferromagnetically inter-plane. The spin-flop field from the antiferromagnetic to ferromagnetic state can be determined by measuring the magnetic field dependence of the susceptibility. For the higher stage sample (stage 3), the inter-plane coupling is very small and the system can be treated like a 2D-ferroma- gnet.