Related papers: Hexatic Phase in Covalent Two-Dimensional Silver I…
In experiments the two-dimensional systems are realized mainly on solid substrates which introduce quenched disorder due to some inherent defects. The defects of substrates influence the melting scenario of the systems and have to be taken…
We study the melting of skyrmions in a two-dimensional Heisenberg chiral magnet with bi-axial Dzyaloshinskii--Moriya interactions. These topological excitations may form at zero temperature a triangular crystal with long-range positional…
We report an extensive Monte-Carlo study of the melting of the classical two dimensional Wigner crystal for a system of point particles interacting via the $1/r$-Coulomb potential. A hexatic phase is found in systems large enough. With the…
This is a set of notes recalling some of the most important results on the XY model from the ground up. They are meant for a junior researcher wanting to get accustomed to the Kosterlitz-Thouless phase transition in the context of the 2D…
We find the complete phase diagram of a generalised XY model that includes half-vortices. The model possesses superfluid, pair-superfluid and disordered phases, separated by Kosterlitz-Thouless (KT) transitions for both the half-vortices…
Monte Carlo simulations of 2D vortex lattice melting in a thin superconducting film (or alternatively an array of Josephson junctions) are performed in the London limit. Finite size scaling analyses are used to make a detailed test of the…
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…
The mixed phase of extremely type-II layered superconductors in perpendicular magnetic field is studied theoretically via the layered XY model with uniform frustration. A partial duality analysis is carried out in the weak-coupling limit.…
We investigated the adsorption of iodine on silver (111) in ultra-high vacuum. Using low-temperature scanning tunneling microscopy (LT-STM) measurements we catalog the complex surface structures on the local scale. We identified three…
Liquid crystals in two dimensions do not support long-ranged nematic order, but a quasi-nematic phase where the orientational correlations decay algebraically is possible. The transition from the isotropic to the quasi-nematic phase can be…
We investigate the ground state phase diagram of the S=1/2 two-leg $XXZ$ spin ladder system with an isotropic interchain coupling. In this model, there is the Berezinskii-Kosterlitz-Thouless transition which occurs at the XY-Haldane and the…
We develop a theory for a novel state of ${}^4$He films, that possesses off diagonal order (as in the superfluid state), as well as hexatic or bond orientational order. Within our description, both the hexatic and superfluid transitions are…
In this article we calculate the surface phase diagram of a two-dimensional hard-rod fluid confined between two hard lines. In a first stage we study the semi-infinite system consisting of an isotropic fluid in contact with a single hard…
The isotropic-to-nematic transition in a two-dimensional fluid of hard needles is studied using grand canonical Monte Carlo simulations, multiple histogram reweighting, and finite size scaling. The transition is shown to be of the…
We study the phase transitions of a restricted solid-on-solid model coupled to an Ising model, which can be derived from the coupled XY-Ising model. There are two kinds of phase transition lines. One is a Ising transition line and the other…
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…
The ground state of the $S=1/2$ $J_{1}-J_{1}$ Heisenberg model on the 2D square lattice with arbitrary signs of exchange constants is considered. States with different spin long-range order types (antiferromagnetic checkerboard, stripe,…
We present diffusion Monte Carlo (DMC) results on a new metastable, superfluid phase above the crystal ground state in two-dimensional 4He at densities > 0.065 1/A^2. The state is anisotropic with hexatic orbital order. This implies that…
Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The…
Based on the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of two-dimensional melting and the analogy between Laughlin states and the two-dimensional one-component plasma (2DOCP), we investigate the possibility of liquid…