Related papers: Two-level correlation function of critical random-…
We study by the perturbative Functional Renormalization Group (FRG) the Random Field and Random Anisotropy O(N) models near $d=4$, the lower critical dimension of ferromagnetism. The long-distance physics is controlled by zero-temperature…
The need for suitable many or infinite fermion correlation functions to describe some low dimensional strongly correlated systems is discussed. This is linked to the need for a correlated basis, in which the ground state may be postive…
A system defined by two coupled Ising models, with a bimodal random field acting in one of them, is investigated. The interactions among variables of each Ising system are infinite-ranged, a limit where mean field becomes exact. This model…
We investigate the effects of randomness in a strongly correlated electron model in one-dimension at half-filling. The ground state correlation functions are exactly written by products of 3$\times$3 transfer matrices and are evaluated…
Using the Matsubara formalism, we consider the massive $(\lambda \phi^{4})_{D}$ vector $N$-component model in the large $N$ limit, the system being confined between two infinite paralell planes. We investigate the behavior of the coupling…
We consider the zero-temperature fixed points controlling the critical behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$, models. We clarify the nature of these fixed points and their stability in the region of…
We show that one can use some renormalized coupling constants to compute the free energy and correlation functions at all critical points of the two-dimensional topological gravity in a uniform way. In particular, one can derive the…
At present, the gauge coupling $\beta$-function in the Standard Model (SM) is known up to four-loop order. As most SM calculations, dimensional regularization was employed. Despite its striking success, other regularization schemes have…
The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at…
We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For…
The interplay and competition of magnetic and superconducting correlations in the weakly interacting two-dimensional Hubbard Model is investigated by means of the functional renormalization group. At zero temperature the flow of…
Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by…
The behavior of the bulk two-point correlation function $G({\bf r};T|d)$ in $d$-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties of the susceptibility in such…
We consider the Ising model on a $d$-dimensional discrete torus of volume $r^d$, in dimensions $d>4$ and for large $r$, in the vicinity of the infinite-volume critical point $\beta_c$. We prove that for $\beta=\beta_c- {\rm const}\,…
An investigation of the performance of the multilevel algorithm in the approach to criticality has been undertaken using the Ising model, performing simulations across a range of temperatures. Numerical results show that the performance of…
The model under consideration is a two-dimensional two-component plasma, i.e., a continuous system of two species of pointlike particles of opposite charges $\pm 1$, interacting through the logarithmic Coulomb interaction. Using the exact…
We report on calculations of smoothed spectral correlations in the two-dimensional Anderson model for weak disorder. As pointed out in (M. Wilkinson, J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing dependence of the…
The critical behavior of the two-dimensional N-vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The beta-functions and critical exponents are calculated in the five-loop approximation, RG…
This tutorial provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). This involves specifying a…
This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic…