Related papers: Critical behavior in topological ensembles
We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of $\lambda(l)-\lambda(\infty) = A l^{-s}$, $l$ being the distance from the surface. We concentrate…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close…
When one of the space-time dimension is compactified on $S^1$, the QCD exhibits the chiral phase transition at some critical radius. When we further turn on a background $\theta$ term which depends on the $S^1$ compactified coordinate, a…
For $d\ge 3$ we construct a new coupling of the trace left by a random walk on a large $d$-dimensional discrete torus with the random interlacements on $\mathbb Z^d$. This coupling has the advantage of working up to macroscopic subsets of…
We calculate model-independently the impact of the critical point on higher order baryon susceptibilities $\chi_n$, showing how they depend on fluctuations of the order parameter. Including all tree level diagrams, we find new contributions…
A spin-orbit coupled quantum wire, with one end proximate to an s-wave superconductor, can become a topological superconductor, with a Majorana mode localized at each end of the superconducting region. It was recently shown that coupling…
Point defects govern many important functional properties of two-dimensional (2D) materials. However, resolving the three-dimensional (3D) arrangement of these defects in multi-layer 2D materials remains a fundamental challenge, hindering…
We explore the critical properties of a topological transition in a two-dimensional, amorphous lattice with randomly distributed points. The model intrinsically breaks the time-reversal symmetry without an external magnetic field, akin to a…
The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…
In this paper we review the theory of unconventional quantum critical points that are beyond the Landau's paradigm. Three types of unconventional quantum critical points will be discussed: (1). The transition between topological order and…
Euclidean invariant Klein-Gordon, Dirac and massive Chern-Simons field theories are constructed in terms of a random walk with a spin factor on a three dimensional lattice. We exactly calculate the free energy and the correlation functions…
We show that critical systems of finite size develop a fractal structure in momentum space with anomalous dimension given in terms of the isotherm critical exponent delta of the corresponding infinite system. The associated power laws of…
We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with…
We present a numerical study of 2D random-bond Potts ferromagnets. The model is studied both below and above the critical value $Q_c=4$ which discriminates between second and first-order transitions in the pure system. Two geometries are…
A chiral $p_x+ip_y$ superconductor on a square lattice with nearest and next-nearest hopping and pairing terms is considered. Gap closures, as various parameters of the system are varied, are found analytically and used to identify the…
The boundary condition dependence of the critical behavior for the three dimensional Anderson transition is investigated. A strong dependence of the scaling function and the critical conductance distribution on the boundary conditions is…
The crystallographic restriction theorem constrains two-dimensional nematicity to display either Ising ($Z_{2}$) or three-state-Potts ($Z_{3}$) critical behaviors, both of which are dominated by amplitude fluctuations. Here, we use group…
We point out some similitudes between the statistics of high Reynolds number turbulence and critical phenomena. An analogy is developed for two-dimensional decaying flows, in particular by studying the scaling properties of the two-point…
Coordination sequences of periodic and quasiperiodic graphs are analysed. These count the number of points that can be reached from a given point of the graph by a number of steps along its bonds, thus generalising the familiar coordination…
We (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ground states to O(n) loop gases; (4) show that the models…