Related papers: O(2) symmetry breaking vs. vortex loop percolation
We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting…
The gauge glass model offers an interesting example of a randomly frustrated system with a continuous O(2) symmetry. In two dimensions, the existence of a glass phase at low temperatures has long been disputed among numerical studies. To…
We postulate the existence of a natural Poissonian marking of the double (touching) points of SLE(6) and hence of the related continuum nonsimple loop process that describes macroscopic cluster boundaries in 2D critical percolation. We…
Emergence of singularity of vorticity at a single point, not related to any symmetry of the initial distribution, has been demonstrated numerically for the first time. Behavior of the maximum of vorticity near the point of collapse closely…
We study a generalized clock model on the simple cubic lattice. The parameter of the model can be tuned such that the amplitude of the leading correction to scaling vanishes. In the main part of the study we simulate the model with $Z_8$…
Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a…
We report thermodynamic values of four-point renormalized coupling constant calculated by Monte Carlo simulations in the continuum limits of the lattice versions of the two-dimensional O(2) and O(3) non-linear sigma models. In each case the…
We investigate by means of Monte Carlo simulation and Finite-Size Scaling analysis the critical properties of the three dimensional O(5) non linear sigma model and of the antiferromagnetic RP2 model, both of them regularized on a lattice.…
The measurements of the magnetic and nematic correlation lengths in a generalization of the two dimensional XY model on the square lattice are presented using classical Monte Carlo simulation. The full phase diagram is re-examined based on…
We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are…
The long-range fields associated with non-abelian vortices generally obstruct full realization, in the spectrum, of the symmetry of the ground state. In the context of 2+1 dimensional field theories, we show how this effect manifests itself…
Recently, it has been suggested that operational properties connected to quantum computation can be alternative indicators of quantum phase transitions. In this work we systematically study these operational properties in 1D systems that…
The vortex state which arises from a projection of SU(2) to $Z_2$ gauge theory is studied at finite temperatures with a special emphasis on the deconfinement phase transition.
The bulk conductivity of a two-dimensional system is studied assuming that quantum interference effects break time-reversal symmetry in the presence of strong spin-orbit interaction and strong lattice potential. The study is carried out by…
Superconductors exhibit unconventional electronic and magnetic properties if the Cooper pair wave function breaks additional symmetries of the normal phase. Rotational symmetries in spin- and orbital spaces, as well as discrete symmetries…
We show that the mechanism of vortex-antivortex pair production via field oscillations, earlier proposed by two of us for systems with first order transitions in presence of explicit symmetry breaking, is in fact very generally applicable.…
The flow past inline oscillating rectangular cylinders is studied numerically at a Reynolds number representative of two-dimensional flow. A symmetric mode, known as S-II, consisting of a pair of oppositely-signed vortices on each side,…
We prove a remarkable combinatorial symmetry in the number of spanning configurations in site percolation: for a large class of lattices, the number of spanning configurations with an odd or even number of occupied sites differs by $\pm 1$.…
An inverse turbulent cascade in a restricted two-dimensional periodic domain leads to the creation of condensate -- a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry on detailed…
We discuss a new type of topological defect in XY systems where the O(2) symmetry is broken in the presence of a boundary. Of particular interest is the appearance of such defects in nanomagnets with a planar geometry. They are manifested…