Related papers: Universal Ratios in the 2-D Tricritical Ising Mode…
Using transfer-matrix extended phenomenological renormalization-group methods the critical properties of spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths ${\vec J}=(J',J',J)$ are studied.…
We calculate the fourth-order cumulant ratio (proposed by Binder) for the two-dimensional Ising model in a strip geometry L x oo. The Density Matrix Renormalization Group method enables us to consider typical open boundary conditions up to…
Our community has a deep and sophisticated understanding of phase transitions and their universal scaling functions. We outline and advocate an ambitious program to use this understanding as an anchor for describing the surrounding phases.…
We study the 3d Ising universality class using the functional renormalisation group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and anti-symmetric…
We derive an exact formula for the corner free-energy contribution of weakly-anisotropic two-dimensional critical systems in the Ising universality class on rectangular domains, expressed in terms of quantities that specify the anisotropic…
We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our…
We analyze a controversial question about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both analytical and numerical studies performed so far support an extended Harris criterion…
We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The…
We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$…
We address the critical and universal aspects of counterion-condensation transition at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling…
In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…
The universal amplitude ratio $R_{\xi}$ for the ($q\leqslant 4$)-state Potts model in two dimensions is determined by using results for the dilute A model in regime 1. The nature of the relationship between the Potts model and the dilute A…
Strongly-interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small…
We consider asymptotics of ratios of random characteristic polynomials associated with orthogonal polynomial ensembles. Under some natural conditions on the measure in the definition of the orthogonal polynomial ensemble we establish a…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $ 6 \le L \le 90 $ in three dimensions with the purpose of verifying the validity of universality for disordered systems. For each…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents…