Universal relaxational dynamics of gapped one-dimensional models in the quantum sine-Gordon universality class

A semiclassical approach to the low-temperature real-time dynamics of generic one-dimensional, gapped models in the sine-Gordon model universality class is developed. Asymptotically exact universal results for correlation functions are obtained in the temperature regime T < Delta, where Delta is the energy gap.     

Large deviation function of the partially asymmetric exclusion process

The large deviation function obtained recently by Derrida and Lebowitz [Phys. Rev. Lett. 80, 209 (1998)] for the totally asymmetric exclusion process is generalized to the partially asymmetric case in the scaling limit. The asymmetry parameter rescales the scaling variable in a simple way. The finite-size corrections to the universal scaling function and the universal cumulant ratio are also obtained to the leading order.     

Nonextensivity at the edge of chaos of a new universality class of one-dimensional unimodal dissipative maps

We introduce a new universality class of one-dimensional unimodal dissipative maps. The new family, from now on referred to as the (z₁, z₂)-logarithmic map, corresponds to a generalization of the z-logistic map. The Feigenbaum-like constants of these maps are determined. It has been recently shown that the probability density of sums of iterates at the edge of chaos of the z-logistic map is numerically consistent with a q-Gaussian, the distribution which, under appropriate constraints, optimizes the nonadditive entropy S_q. We focus here on the presently generalized maps to check whether they constitute a new universality class with regard to q-Gaussian attractor distributions. We also study the generalized q-entropy production per unit time on the new unimodal dissipative maps, both for strong and weak chaotic cases. The q-sensitivity indices are obtained as well. Our results are, like those for the z-logistic maps, numerically compatible with the q-generalization of a Pesin-like identity for ensemble averages.     

Large deviation function for the current in the open asymmetric simple exclusion process

We consider the one-dimensional asymmetric exclusion process with particle injection and extraction at two boundaries. The model is known to exhibit four distinct phases in its stationary state. We analyze the current statistics at the first site in the low and high density phases. In the limit of infinite system size, we conjecture an exact expression for the current large deviation function.     

Sloppy-model universality class and the Vandermonde matrix

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy: the system behavior depends only on a few "stiff" combinations of the parameters and is unchanged as other "sloppy" parameter combinations vary by orders of magnitude. We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.     

Evidence for an unconventional universality class from a two-dimensional dimerized quantum heisenberg model

The two-dimensional J-J' dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio alpha=J'/J. The critical point of the order-disorder quantum phase transition in the J-J' model is determined as alpha_c=2.5196(2) by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the J-J' model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.     

On the universality class of the 3d Ising model with long-range-correlated disorder

We analyze a controversial topic about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both theoretical and numerical studies agree on the validity of the extended Harris criterion [A. Weinrib, B.I. Halperin, Phys. Rev. B 27 (1983) 413] and indicate the existence of a new universality class, numerical values of the critical exponents found so far differ considerably. To resolve this discrepancy we perform extensive Monte Carlo simulations of a 3d Ising model with non-magnetic impurities being arranged in a form of lines along randomly chosen axes of a lattice. The Swendsen-Wang algorithm is used alongside with a histogram reweighting technique and finite-size scaling analysis to evaluate the values of critical exponents governing magnetic phase transition. Our estimates for these exponents differ from both previous numerical simulations and are in favor of a non-trivial dependency of the critical exponents on the peculiarities of long-range correlation decay.     

Quantitative universality for a class of nonlinear transformations

A large class of recursion relationsx _{n + 1} = f(x_n) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximum . With sufficiently small),z > 1, the universal details depend only uponz. In particular, the local structure of high-order stability sets is shown to approach universality, rescaling in successive bifurcations, asymptotically by the ratio ( = 2.5029078750957... forz = 2). This structure is determined by a universal functiong ^*(x), where the 2ⁿth iterate off,f ⁽ⁿ⁾, converges locally to ^–n g ^*( ⁿ x) for largen. For the class off's considered, there exists a _n such that a 2ⁿ-point stable limit cycle including exists; – _n R~ ^–n ( = 4.669201609103... forz = 2). The numbers and have been computationally determined for a range ofz through their definitions, for a variety off's for eachz. We present a recursive mechanism that explains these results by determiningg ^* as the fixed-point (function) of a transformation on the class off's. At present our treatment is heuristic. In a sequel, an exact theory is formulated and specific problems of rigor isolated.Research performed under the auspices of the U.S. Energy Research and Development Administration.     

The two-point correlation function of the one-dimensional matrix model

Following Kostov and Ben-Menahem, we calculate the two-puncture correlation function for the one-dimensional matrix model. We find that it depends on the details of discretization for all momenta p. Its only universal features are its vanishing as p → 0 and the appearance of double poles at |p| = n/√′, N = 1,2,…. We show how to derive these double poles in the conformal gauge treatment of Liouville gravity.     

Large Higgs mass and μ−e universality

In the limit of very large Higgs mass the Weinberg model becomes non-renormalizable, and this, in principle, provides for an upper limit on the Higgs mass. In actual fact, without further speculation, no useful limit emerges. Instead one is led to speculations on direct lepton hadron interactions violating μ?e universality. The experimental evidence on this point is considered.     

Scaling behavior of the directed percolation universality class

In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling behavior, we present clear numerical evidence that all models belong to the universality class of directed percolation. Since the considered models are characterized by different interaction details the obtained universal scaling plots are an impressive manifestation of the universality of directed percolation.     

Large deviation statistics of the energy-flux fluctuation in the shell model of turbulence

The energy-flux fluctuation in the shell model of turbulence is numerically analyzed from the large deviation statistical point of view. We first observe that the rate function defined in the inertial range is independent of the Reynolds number. The rate function derived by the cascade model of the log-Poisson statistics turns out to be in good agreement with the present numerical result in the region where strong singularity of fluctuation exits. This fact may imply the universality as well as the robustness of the large deviation statistical quantities in turbulence.     

New universality class for the three-dimensional XY model with correlated impurities: application to 4He in aerogels

Encouraged by experiments on 4He in aerogels, we confine planar spins in the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behavior of the three-dimensional XY model. Monte Carlo simulations and finite-size scaling are used to determine critical couplings K(c) and exponents. In agreement with experiments, clear evidence of change in the thermal critical exponents nu and alpha is found at nonzero volume fractions of impurities. These changes are explained in terms of hidden long-range correlations within disorder distributions.     

On the universality class of certain string theory hadrons

Exploiting the gauge/gravity correspondence we find the spectrum of hadronic-like bound states of adjoint particles with a large global charge in several confining theories. In particular, we consider an embedding of four-dimensional N=1 supersymmetric Yang–Mills into IIA string theory, two classes of three-dimensional gauge theories and the softly broken version of one of them. In all cases we describe the low energy excitations of a heavy hadron with mass proportional to its global charge. These excitations include: the hadron's nonrelativistic motion, its stringy excitations and excitations corresponding to the addition of massive constituents. Our analysis provides ample evidence for the universality of such hadronic states in confining theories admitting supergravity duals. Besides, we find numerically a new smooth solution that can be thought of as a nonsupersymmetric deformation of G₂ holonomy manifolds.     

Short-time behavior of the vibrational-energy-time correlation function for a one-dimensional model of diatomic molecules

The short-time behavior of the vibrational-energy-time correlation function (VECF) is studied both theoretically and numerically for a one-dimensional model of diatomic molecules with harmonic intramolecular and hard intermolecular interactions. In the equipartition regime, the short-time expansion of the VECF is independent of the vibrational frequency and agrees with statistical mechanics.