Related papers: Random percolation as a gauge theory
We study the behaviour of the monopole at finite temperature in the (2+1)-dimensional lattice gauge theory dual to the percolation model; by exploiting the correspondences to statistical systems, we possess powerful tools to evaluate the…
The behaviour of the space-like string tension in the high temperature phase is studied. Data obtained in the $Z_2$ gauge model in (2+1) dimensions are compared with predictions of a simple model of a fluctuating flux tube with finite…
We discuss the physical picture of thick vortices as the mechanism responsible for confinement at arbitrarily weak coupling in SU(2) gauge theory. By introducing appropriate variables on the lattice we distinguish between thin, thick and…
We present further evidence for the bulk nature of the phase transition line in the fundamental--adjoint action plane of SU(3) lattice gauge theory. Computing the string tension and some glueball masses along the thermal phase transition…
We describe infinite clusters which arise in nearest-neighbour percolation for so-called cocycle measures on the square lattice. These measures arise naturally in the study of random transformations. We show that infinite clusters have a…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
Three-dimensional three-colour percolation on a lattice made of tetrahedra is a direct generalization of two-dimensional two-colour percolation on the triangular lattice. The interfaces between one-colour clusters are made of bicolour…
The upper estimate of the percolation threshold of the Bernoulli random field on the hexagonal lattice is found. It is done on the basis of the cluster decomposition. Each term of the decomposition is estimated using the number estimate of…
The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…
Causality constrains the gravitational interactions of massive higher spin particles in both AdS and flat spacetime. We explore the extent to which these constraints apply to composite particles, explaining why they do not rule out…
We study percolation and the random cluster model on the triangular lattice with 3-body interactions. Starting with percolation, we generalize the star--triangle transformation: We introduce a new parameter (the 3-body term) and identify…
Yang-Mills theories undergo a deconfining phase transition at a critical temperature. In lattice calculations the temporal Wilson loop and Z_3 order parameter show above this temperature a behavior typical of deconfinement. A quantity of…
The normal confining phase of gauge theories is characterised by the condensation of magnetic monopoles and center vortices. Sometimes in coupled gauge system one finds another phase with simultaneous condensation of electric and magnetic…
We make a numerical study of the finite temperature properties of the SO(3) lattice gauge theory. As its symmetry properties are quite different from those of the SU(2) LGT, a different set of observables have to be considered in this…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…
We examine SU(2) gauge theory in 3+1 dimensions at finite temperature in the vicinity of critical point. For various lattice sizes in time direction ($N_\tau=1,2,4,8$) we extract high precision values of the inverse critical coupling and…
We calculate Wilson loops of various sizes up to 20 loops in SU(3) pure lattice gauge theory at different lattice sizes for Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate…
We emphasize that non-conformal theories provide a natural playground for the ideas of the Maldacena conjecture, opening the possibility of exploring properties that could potentially be in the same universality class as QCD. In particular,…
Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts…
In this article, we revisit random site and bond percolation in square lattice focusing primarily on the behavior of entropy and order parameter. In the case of traditional site percolation, we find that both the quantities are zero at…