Related papers: First-order and Berezinskii-Kosterlitz-Thouless ph…
We study phase transitions in $XY$ models, generalized by inclusion of $n$ higher-order pairwise interactions of equal strength, by Monte Carlo simulation. It is found that by adding new terms the Berezinskii-Kosterlitz-Thouless (BKT)…
We study the two-dimensional generalized XY model that depends on an integer $q$ by the Monte Carlo method. This model was recently proposed by Romano and Zagrebnov. We find a single Kosterlitz-Thouless (KT) transition for all values of…
The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we…
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…
Critical behavior of the two-dimensional generalized $XY$ model involving solely nematic-like terms of the second, third and fourth orders is studied by Monte Carlo method. We find that such a system can undergo three successive phase…
We propose two machine-learning methods based on neural networks, which we respectively call the phase-classification method and the temperature-identification method, for detecting different types of phase transitions in the XXZ models…
We consider the two-dimensional classical XY model on a square lattice in the thermodynamic limit using tensor renormalization group and precisely determine the critical temperature corresponding to the Berezinskii-Kosterlitz-Thouless (BKT)…
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 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…
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 use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase…
We study the two-dimensional XY model with quenched random phases by Monte Carlo simulation and finite-size scaling analysis. We determine the phase diagram of the model and study its critical behavior as a function of disorder and…
We consider the classical XY model (or classical rotor model) on the two-dimensional square lattice graph as well as its dual model, which is a model of height functions. The XY model has a phase transition called the…
We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two bond ordered phases, one with local ferromagnetic…
The classical XY model has been consistently studied since it was introduced more than six decades ago. Of particular interest has been the two-dimensional spin model's exhibition of the Berezinskii-Kosterlitz-Thouless (BKT) transition.…
We investigate the phase diagram of a two-dimensional driven-dissipative system of polaritons coupled to the excitonic reservoir. We find that two critical points exists. The first corresponds to the quasi-condensation and the second to a…
Two dimensional systems with U(1) symmetry exhibit a peculiar phase, i.e., the Berezinskii-Kosterlitz-Thouless (BKT) phase. In particular situations, the BKT phase exists as an intermediate temperature phase. There have been scenarios for…
We consider the 2D $J_1-J_2$ classical XY model on a square lattice. In the frustrated phase corresponding to $J_2>J_1/2$, an Ising like order parameter emerges by an ``order due to disorder'' effect. This leads to a discrete $Z_2$ symmetry…
We investigate the two-dimensional classical Heisenberg model with a nonlinear nearest-neighbor interaction V(s,s')=2K[(1+s.s')/2 ]^p. The analogous nonlinear interaction for the XY model was introduced by Domany, Schick, and Swendsen, who…
The $q-$state clock model, sometimes called the discrete $XY$ model, is known to show a second-order (symmetry breaking) phase transition in two-dimension (2D) for $q\le 4$ ($q=2$ corresponds to the Ising model). On the other hand, the…