Related papers: Self-Consistent Scaling Theory for Logarithmic Cor…
Conformal field theories with correlation functions which have logarithmic singularities are considered. It is shown that those singularities imply the existence of additional operators in the theory which together with ordinary primary…
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…
Lattice models of coupled dynamical systems lead to a variety of complex behaviors. Between the individual motion of independent units and the collective behavior of members of a population evolving synchronously, there exist more…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
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…
Quantum critical systems with multiple dynamics possess not only one but several time scales, tau_i ~ xi^(z_i), which diverge with the correlation length xi. We investigate how scaling predictions are modified for the simplest case of…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
This paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under…
The vapor-liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions, $L$, focusing on periodic boundary conditions, as appropriate for simulations. The recently propounded ``complete''…
Critical phenomena in non-equilibrium systems have been studied by means of a wide variety of theoretical and experimental approaches. Mode-coupling, renormalization group, complex Lie algebras and diagrammatic techniques are some of the…
A recurring task in particle physics and statistics is to compute the complex critical points of a product of powers of affine-linear functions. The logarithmic discriminant characterizes exponents for which such a function has a degenerate…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
Low-energy remnant fundamental symmetry violations may be present in nature at levels attainable in upcoming experiments. These effects may arise through spontaneous symmetry breaking in a more complete Lorentz covariant theory underlying…
At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We study the dynamics of the critical two-dimensional fully-frustrated Ising model by means of Monte Carlo simulations. The dynamical exponent is estimated at equilibrium and is shown to be compatible with the value $z_c=2$. In a second…
Long-range quantum lattice systems often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent…
The paper that is commented by Touchette contains a computational study which opens the door to a desirable generalization of the standard large deviation theory (applicable to a set of $N$ nearly independent random variables) to systems…
In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, characterized by smooth behavior of key quantities, and the critical region, where these quantities exhibit…
We analyze the probabilities of large infrequent fluctuations in systems driven by external fields. In a broad range of the field magnitudes, the logarithm of the fluctuation probability is linear in the field magnitude, and the response…