Related papers: Self-Consistent Scaling Theory for Logarithmic Cor…
Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such…
By the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical…
We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper…
We analyze the scaling and finite-size-scaling behavior of the two-dimensional 4-state Potts model. We find new multiplicative logarithmic corrections for the susceptibility, in addition to the already known ones for the specific heat. We…
We study various corrections of correlation functions to leading order in conformal perturbation theory, both on the cylinder and on the plane. Many problems on the cylinder are mathematically equivalent to those in the plane if we give the…
We use an analytic toy model of turbulent convection to show that most of the scaling regimes are spoiled by logarithmic corrections, in a way consistent with the most accurate experimental measurements available nowadays. This sets a need…
There are two independent critical exponents that describe the behavior of systems near their critical point. However, at the critical point only the exponent $\eta$, which describes the decay of the correlation function, is usually…
The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating…
We describe an approach to logarithmic conformal field theories as limits of sequences of ordinary conformal field theories with varying central charge c. Logarithmic behaviour arises from degeneracies in the spectrum of scaling dimensions…
The analysis of correlation function data obtained by Monte Carlo simulations of the two-dimensional 4-state Potts model, XY model, and self-dual disordered Ising model at criticality are presented. We study the logarithmic corrections to…
The method of self-similar root approximants has earlier been shown to provide accurate interpolating formulas for functions for which small-variable expansions are given and the behaviour of the functions at large variables is known. Now…
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…
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…
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…
Low temperature dynamics of the S=1/2 Heisenberg chain is studied via a simple ansatz generalizing the conformal mapping and analytic continuation procedures to correlation functions with multiplicative logarithmic factors. Closed form…
Monte Carlo (MC) and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the two-dimensional 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic…
A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic…
For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such…
Using thermodynamic arguments treatment it is shown that, independently on whether Fisher renormalization changes the critical exponents near a phase transition in a constrained system or not, new corrections to scaling with correction…
Logarithmic operators and logarithmic conformal field theories are reviewed. Prominent examples considered here include c=-2 and c=0 logarithmic conformal field theories. c=0 logarithmic conformal field theories are especially interesting…