Related papers: Critical behavior of systems with long-range inter…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
Scaling and hyperscaling laws provide exact relations among critical exponents describing the behavior of a system at criticality. For nonequilibrium growth models with a conserved drift there exist few of them. One such relation is $\alpha…
We investigate the modification of discrete scale invariance in the bound state spectrum by long-range interactions. This problem is relevant for effective field theory descriptions of nuclear cluster states and manifestations of the Efimov…
Scaling, hyperscaling and finite-size scaling were long considered problematic in theories of critical phenomena in high dimensions. The scaling relations themselves form a model-independent structure that any model-specific theory must…
We investigate the critical behavior of the lambda phi^4 theory defined on S^1 x R^d having two finite length scales beta, the circumference of S^1, and k^{-1}, the blocking scale introduced by the renormalization group transformation. By…
We study the behavior of two spatially distributed (sandpile) models which are weakly linked with one another. Using a Monte-Carlo implementation of the renormalization group and algebraic methods, we describe how large-scale correlations…
We discuss finite-size effects in one disordered ${\lambda}{\phi}^{4}$ model defined in a $d$-dimensional Euclidean space. We consider that the scalar field satisfies periodic boundary conditions in one dimension and it is coupled with a…
The long-time behaviour of spin-spin correlators in the slow relaxation of systems undergoing phase-ordering kinetics is studied in geometries of finite size. A phenomenological finite-size scaling ansatz is formulated and tested through…
The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and…
We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the…
The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method. The finite-size crossover in impure films has been considered on the basis of the…
The influence of a thermodynamic constraint on the critical finite-size scaling behavior of three-dimensional Ising and XY models is analyzed by Monte-Carlo simulations. Within the Ising universality class constraints lead to Fisher…
A non-perturbative Renormalization Group approach is used to calculate scaling functions for an O(4) model in d=3 dimensions in the presence of an external symmetry-breaking field. These scaling functions are important for the analysis of…
We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L^{5/4}, rather than proportional to L as in standard finite size scaling (FSS) theory. Our results confirm a…
The process of adsorption on a planar repulsive, "marginal" and attractive wall of long-flexible polymer chains with excluded volume interactions is investigated. The performed scaling analysis is based on formal analogy between the polymer…
Collective behaviour in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological…
The dynamical properties of a dense horizontally vibrated bidisperse granular monolayer are experimentally investigated. The quench protocol produces states with a frozen structure of the assembly, but the remaining degrees of freedom…
We analyze the critical behavior of isotropic systems with dipole-dipole interaction by renormalization-group methods in fixed space-time dimensions. Working in three-dimensional theory we analytically find three-loop expressions for…
DNA denaturation, wetting in two dimensions, depinning of a flux line, and other problems map onto a phase transition with effective long range interaction. It yields giant non-universal critical indexes, arbitrarily large macroscopic…
The critical scaling of the large-$N$ $O(N)$ model in higher dimensions using the exact renormalization group equations has been studied, motivated by the recently found non-trivial fixed point in $4<d<6$ dimensions with metastable critical…