Related papers: New insight into the Berezinskii-Kosterlitz-Thoule…
The 2d XY model exhibits an essential phase transition, which was predicted long ago --- by Berezinskii, Kosterlitz and Thouless (BKT) --- to be driven by the (un)binding of vortex--anti-vortex pairs. This transition has been confirmed for…
We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly…
In statistical physics, the XY model in two dimensions provides the paradigmatic example of phase transitions mediated by topological defects (vortices). Over the years, a variety of analytical and numerical methods have been deployed in an…
The Berezinskii-Kosterlitz-Thouless (BKT) essential phase transition in the 2d XY model is revisited. Its mechanism is usually described by the (un)binding of vortex--anti-vortex (V--AV) pairs, which does, however, not provide a clear-cut…
Evidence for a Kosterlitz-Thouless transition in the 2D step model is obtained from Monte Carlo determinations of the helicity modulus. It is argued that the free energy of a single vortex at the center of the system depends logarithmically…
The Berezinskii-Kosterlitz-Thouless mechanism, in which a phase transition is mediated by the proliferation of topological defects, governs the critical behaviour of a wide range of equilibrium two-dimensional systems with a continuous…
We investigate the nature of the phase transition occurring in a planar XY-model spin system with dipole-dipole interactions. It is demonstrated that a Berezinskii-Kosterlitz-Thouless (BKT) type of phase transition always takes place at a…
We examine the Kosterlitz-Thouless universality class and show that essential scaling at this type of phase transition is not self-consistent unless multiplicative logarithmic corrections are included. In the case of specific heat these…
We employ a novel, unbiased renormalization-group approach to investigate non-equilibrium phase transitions in infinite lattice models. This allows us to address the delicate interplay of fluctuations and ordering tendencies in low…
A paradigmatic example of a phase transition taking place in the absence of symmetry-breaking is provided by the Berezinkii-Kosterlitz-Thouless (BKT) transition in the two-dimensional XY model. In the framework of canonical ensemble, this…
We investigate the out of equilibrium dynamics of the two-dimensional XY model when cooled across the Berezinskii-Kosterlitz-Thouless (BKT) phase transition using different protocols. We focus on the evolution of the growing correlation…
In tensor network representation, the partition function of a generalized two-dimensional XY spin model with topological integer and half-integer vortex excitations is mapped to a tensor product of one-dimensional quantum transfer operator,…
The critical behavior of the two-dimensional XY model has been explored in the literature using various methods. They include the high-temperature expansion (HTE) method, Monte Carlo (MC) approach, strong coupling expansion method, and…
The modified XY model is a variation of the XY model extended by a half periodic term, exhibiting a rich phase structure. As the Goldstone model, also known as the linear O(2) model, can be obtained as a continuum and regular model for the…
We have considered two classical lattice-gas models, consisting of particles that carry multicomponent magnetic momenta, and associated with a two-dimensional square lattices; each site can host one particle at most, thus implicitly…
The aim of this paper is to illustrate that generalized two-dimensional XY models (proposed by Romano and Zagrebnov) may also support a first-order phase transition. Two approaches are employed to accurately determine the critical parameter…
Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii--Kosterlitz--Thouless phase transitions of the two-dimensional (2D) classical $XY$ and the 2D generalized classical…
We perform Monte Carlo simulations to study the two dimensional random-bond XY model on a square lattice. Two kinds of bond randomness with the coupling coefficient obeying the Gaussian or uniform distribution are discussed. It is shown…
In this paper, we thoroughly examined the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional XY model on the honeycomb lattice. To address its thermodynamical behavior, we combined standard numerical Monte Carlo…
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 transition associated…