Related papers: Generic critical points of normal matrix ensembles
We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically…
In a seminal paper, Viana built examples of maps presenting two positive Lyapunov exponents exploring skew-products of a (uniformly) expanding map and a quadratic map (order 2 critical point) perturbed by some level of noise. Here we extend…
We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…
(shortened) We determine the transformation matrix T that maps multiple images with resolved features onto one another and that is based on a Taylor-expanded lensing potential close to a point on the critical curve within our…
We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…
We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's…
We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of…
We further study the interfaces arising in a situation of inhomogeneity. More precisely, we identify a characteristic length for the gradient percolation model, that enables us to tighten previous estimates established for it. This allows…
Rectangular $N\times M$ matrix models can be solved in several qualitatively distinct large $N$ limits, since two independent parameters govern the size of the matrix. Regarded as models of random surfaces, these matrix models interpolate…
We consider the relation between three physical problems: 2D directed lattice random walks, ensembles of $T_{n,n+1}$ torus knots, and instanton ensembles in 5D SQED with one compact dimension in $\Omega$ background and with 5D Chern-Simons…
We study the variational behavior of the total inverse mean curvature of curves with prescribed boundary in the half-plane. We characterize the existence of critical points with prescribed area. We show that such critical points are…
The evolution pattern of level crossings and exceptional points is studied in a non-integrable pairing model with two different integrable limits. One of the integrable limits has two independent parameter-dependent integrals of motion. We…
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…
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…
The second-order phase transitions in the Ising model and liquid-gas systems share a universality class and critical exponents, despite the absence of $Z_2$ symmetry in the liquid-gas Hamiltonian. This discrepancy highlights a central…
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…
Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions…
We deal with the following closely related problems: (i) For a germ of a reduced plane analytic curve, what is the minimal degree of an algebraic curve with a singular point analytically equivalent (isomorphic) to the given one? (ii) For a…
In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum…