Related papers: Fisher's scaling relation above the upper critical…
We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the…
We write exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional…
A model of the passive vector quantity advected by a Gaussian time-decorrelated self-similar velocity field is studied; the effects of pressure and large-scale anisotropy are discussed. The inertial-range behavior of the pair correlation…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as $1/r^{d+\sigma}$, where $d$ is the spatial dimension and the long-range parameter $\sigma>0$.…
We show that when the dynamical dimension of the $\bar{\psi}\psi$ operator is reduced from three to two in a fermion electrodynamics with scaling, a $g(\bar{\psi}\psi)^2+g(\bar{\psi}i\gamma^5\psi)^2$ four-fermion interaction which is…
The finite-size scaling (FSS) theory for continuous phase transitions has been useful in determining the critical behavior from the size dependent behaviors of thermodynamic quantities. When the phase transition is discontinuous, however,…
We devise a geometric description of bounded systems at criticality in any dimension $d$. This is achieved by altering the flat metric with a space dependent scale factor $\gamma(x)$, $x$ belonging to a general bounded domain $\Omega$.…
It is argued that the Thouless number g(L) is not the only parameter relevant in scale transformations, and that the second parameter connected with off-diagonal disorder should be introduced. A two-parameter scaling theory is suggested…
Dimensional correspondences have a long history in critical phenomena. Here, we review the effective dimension approach, which relates the scaling exponents of a critical system in $d$ spatial dimensions with power-law decaying interactions…
We write exact renormalization-group recursion relations for a ferromagnetic Ising model on the diamond hierarchical lattice with an aperiodic distribution of exchange interactions according to a class of generalized two-letter Fibonacci…
The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order…
In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of…
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling…
Numerical results for Anderson transition are critically discussed. A simple procedure to deal with corrections to scaling is suggested. With real uncertainties taken into account, the raw data are in agreement with a value $\nu=1$ for the…
A model of the passive vector field advected by the uncorrelated in time Gaussian velocity with power-like covariance is studied by means of the renormalization group and the operator product expansion. The structure functions of the…
Non-equilibrium diffusive systems are known to exhibit long-range correlations, which decay like the inverse 1/L of the system size L in one dimension. Here, taking the example of the ABC model, we show that this size dependence becomes…
We study the density of specular reflection points in the geometrical optics limit when light scatters off fluctuating interfaces and membranes in thermodynamic equilibrium. We focus on the statistical mechanics of both capillary-gravity…
We calculate the fractal dimension $d_{\rm f}$ of critical curves in the $O(n)$ symmetric $(\vec \phi^2)^2$-theory in $d=4-\varepsilon$ dimensions at 6-loop order. This gives the fractal dimension of loop-erased random walks at $n=-2$,…