Holographic Berezinskii-Kosterlitz-Thouless Transitions

Berezinskii-Kosterlitz-Thouless transition of two-component Bose mixtures with inter-component Josephson coupling

We study the Berezinskii-Kosterlitz-Thouless (BKT) transition of two-component Bose mixtures in two spatial dimensions. When phases of both components are decoupled, half-quantized vortex-antivortex pairs of each component induce two-step BKT transitions. On the other hand, when phases of the both components are synchronized through the inter-component Josephson coupling, two species of vortices of each component are bind to form a molecule, and in this case, we find that there is only one BKT transition by molecule-antimolecule pairs. Our results can be tested by two weakly-connected Bose sys…

Noncommutative X-Y model and Kosterlitz Thouless transition

Matrix models have been shown to be equivalent to noncommutative field theories. In this work we study noncommutative X-Y model and try to understand Kosterlitz Thouless transition in it by analysing the equivalent matrix model. We consider the cases of a finite lattice and infinite lattice separately. We show that the critical value of the matrix model coupling is identical for the finite and infinite lattice cases. However, the critical values of the coupling of the continuum field theory, in the large $ N $ limit, is finite in the infinite lattice case and zero in the case of finite lattice…

二维超流体中的Kosterlitz-Thouless相变

Kosterlitz-Thouless transition in two-dimensional superfluid

本文研究了二维超流体中由相位涨落驱动的Kosterlitz-Thouless相变，结合Monte Carlo模拟与基于Goldstone模式有效理论的解析方法进行分析。

Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model

We introduce and study the properties of a periodic model interpolating between the sine-- and the sinh--Gordon theories in $1+1$ dimensions. This model shows the peculiarities, due to the preservation of the functional form of their potential across RG flows, of the two limiting cases: the sine-Gordon, not having conventional order/magnetization at finite temperature, but exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the sinh-Gordon, not having a phase transition, but being integrable. The considered interpolation, which we term as {\em sn-Gordon} model, is performed with p…

Finite Temperature Bosonic Closed Strings: Thermal Duality and the Kosterlitz Thouless Transition

We elucidate the properties of a gas of free closed bosonic strings in thermal equilibrium. Our starting point is the intensive generating functional of connected one-loop closed vacuum string graphs given by the Polyakov path integral. Invariance of the path integral under modular transformations gives a thermal duality invariant expression for the free energy of free closed strings at finite temperature. The free bosonic string gas exhibits a self-dual Kosterlitz-Thouless phase transition. The thermodynamic potentials of the gas of free bosonic closed strings are shown to exhibit an infinite…

Planar Superconductivity via Kosterlitz-Thouless mechanism

The phase structure of a $(2+1)$ - dimensional model of relativistic fermions with a four fermi interaction is analyzed in the strong coupling regime using the large $N$ perturbation theory. It is shown that, this model exhibits a low temperature superconducting phase due to the vortex-anti vortex binding via Kosterlitz-Thouless mechanism. Above a critical temperature, vortices unbind and superconductivity is destroyed; at a still higher temperature the vacuum expectation value of a neutral order parameter vanishes. The ground state respects parity and time reversal symmetries.

Kosterlitz-Thouless Phase Transition In The Two Dimensional Linear Sigma Model

We investigate the O(N) symmetric linear $σ$-model in two dimensions by means of an exact nonperturbative evolution equation. The perturbative infrared divergences are absent in this formulation. We use a simple approximative solution of the flow equation which corresponds to a derivative expansion for the effective action. For N=2 this gives a good picture of the Kosterlitz-Thouless phase transition.

Quantum Berezinskii-Kosterlitz-Thouless transition in the superconducting phase of (2+1)-dimensional quantum chromodynamics

We study superconductivity in the hadron-quark mixed phase of planar quantum chromodynamics (QCD) within the large $N$ limit of a Gross-Neveu model modified by a repulsive vector term. At high densities, the combination of scalar attraction and repulsive space-like part of the vector interaction squeezes quarks into baryonic composite states, i.e., Dirac fermions with even numbers of bosonic vortices attached. The time-like vector component induces Cooper pairing between these Fermi surface modes. Remarkably, at zero temperature, competition between the quark density and mass destroys supercon…

The Kosterlitz-Thouless Phenomenon on a Fluid Random Surface

The problem of a periodic scalar field on a two-dimensional dynamical random lattice is studied with the inclusion of vortices in the action. Using a random matrix formulation, in the continuum limit for genus zero surfaces the partition function is found exactly, as a function of the chemical potential for vortices of unit winding number, at a specific radius in the plasma phase. This solution is used to describe the Kosterlitz- Thouless phenomenon in the presence of 2D quantum gravity as one passes from the ultra-violet to the infra-red.

二维体系中的伯泽林-科斯特利茨-托勒斯量子相变

Berezinskii-Kosterlitz-Thouless quantum transition in 2 dimensions

本文研究了二维量子系统中由耦合常数驱动的零温度量子BKT相变，其具有与量子格里菲斯相变相同的发散指数，但不涉及无序。

Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition

The Kosterlitz-Thouless phase transition is described by the nonperturbative renormalization flow of the two dimensional $ϕ^4$-model. The observation of essential scaling demonstrates that the flow equation incorporates nonperturbative effects which have previously found an alternative description in terms of vortices. The duality between the linear and nonlinear $σ$-model gives a unified description of the long distance behaviour for O(N)-models in arbitrary dimension $d$. We compute critical exponents in first order in the derivative expansion.