Related papers: Universality classes for unstable crystal growth
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
The renowned general epidemic process describes the stochastic evolution of a population of individuals which are either susceptible, infected or dead. A second order phase transition belonging to the universality class of dynamic isotropic…
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 prove the existence of solution for a class of $p(x)$-Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic…
We develop a general framework to study hyperuniformity of various mathematical models of quasicrystals. Using this framework we provide examples of non-hyperuniform quasicrystals which unlike previous examples are not limit-quasiperiodic.…
Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Euler equations, develop infinite gradients from smooth initial…
Cascading failures may lead to dramatic collapse in interdependent networks, where the breakdown takes place as a discontinuity of the order parameter. In the cascading failure (CF) model with healing there is a control parameter which at…
We study the static and dynamic behavior of the one dimensional pair contact process with diffusion. Several critical exponents are found to vary with the diffusion rate, while the order-parameter moment ratio m=\bar{rho^2} /\bar{rho}^2…
We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders. If the multiplication operators $B_{1,2}$ tend to differential operators of order $l_{2,1}$, respectively, the singularity is…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
We introduce a new method for the analysis of singularities in the unstable problem $$\Delta u = -\chi_{\{u>0\}},$$ which arises in solid combustion as well as in the composite membrane problem. Our study is confined to points of…
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…
The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\times 2$ Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization…
Recent experiments and simulations have shown that unsteady turbulent flows, before reaching a dynamic equilibrium state, display a universal behaviour. We show that the observed universal non-equilibrium scaling can be explained using a…
All (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices belong to the same universality class, in the sense that they have identical critical exponents at the critical point (assuming the exponents…
Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is…
Clusters and droplets of positive spins in the two-dimensional Ising model percolate at the Curie temperature in absence of external field. The percolative exponents coincide with the magnetic ones for droplets but not for clusters. We use…
We identify a new universality class of phase transitions that emerges in non-normal systems, extending the classical framework beyond eigenvalue instabilities. Unlike traditional critical phenomena, where transitions occur when eigenvalues…
Motivated by recent experimental studies in microbiology, we suggest a modification of the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its…
Recently Carlon et. al. investigated the critical behavior of the pair contact process with diffusion [cond-mat/9912347]. Using density matrix renormalization group methods, they estimate the critical exponents, raising the possibility that…