Related papers: Generalized scaling theory for critical phenomena …
A new set of infinitesimal transformations generalizing scale invariance for strongly anisotropic critical systems is considered. It is shown that such a generalization is possible if the anisotropy exponent \theta =2/N, with N=1,2,3 ...…
Conventional ordering transitions, described by the Landau paradigm, are characterized by the symmetries broken at the critical point. Within the constrained manifold occurring at low temperatures in certain frustrated systems,…
Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only…
Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only…
Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when…
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…
In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system.…
Phase transitions, as one of the most intriguing phenomena in nature, are divided into first-order phase transitions (FOPTs) and continuous ones in current classification. While the latter shows striking phenomena of scaling and…
Scale invariance and the resulting power law behaviours are seen in diverse systems. In this work we consider translation, rotational and scale invariant systems defined on a lattice, such that the variables defining the state at every…
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…
Phase transitions and critical phenomena are among the most intriguing phenomena in nature and their renormalization-group theory is one of the greatest achievements of theoretical physics. However, the predictions of the theory above an…
We discuss a scaling theory of the lattice response in the vicinity of a finite-temperature critical end point. The thermal expansivity is shown to be more singular than the specific heat such that the Gr\"uneisen ratio diverges as the…
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…
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 derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
Boundary critical phenomena are studied in the 3- State Potts model in 2 dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary conditions is obtained using both fusion and…
Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only…
Under quite general conditions critical phenomena can be described with high order linked cluster expansions. The coefficients of the series admit a graphical expansion that is generated with the aid of computers. Our generalization of…
This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their…
It is demonstrated that the scaled order parameter for ferromagnetic Ising and three-state Potts chains with inverse-square interactions exhibits a universal critical jump, in analogy with the superfluid density in helium films.…