Two-particle correlation length in fireball models

It is pointed out that all models in which particle production occurs via an intermediate step of isotropically decaying fireballs, predict the existence of the positive short-range component in two-particle inclusive correlations. The correlation lenght is predicted to be about one, in agreement with existing data.     

Phase uniqueness and correlation length in diluted-field Ising models

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim _n-(1/n) log ₀; _n)^-1, wheren is the site on the first coordinate axis at distancen from the origin and ₀; _n is the origin ton two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .     

Scattering length scaling laws for ultracold three-body collisions

We present a simple and unifying picture that provides the energy and scattering length dependence for all inelastic three-body collision rates in the ultracold regime for three-body systems with short-range two-body interactions. Here, we present the scaling laws for vibrational relaxation, three-body recombination, and collision-induced dissociation for systems that support s-wave two-body collisions. These systems include three identical bosons, two identical bosons, and two identical fermions. Our approach reproduces all previous results, predicts several others, and gives the general form of the scaling laws in all cases.     

Dynamical scaling in branching models for seismicity

We propose a branching process based on a dynamical scaling hypothesis relating time and mass. In the context of earthquake occurrence, we show that experimental power laws in size and time distribution naturally originate solely from this scaling hypothesis. We present a numerical protocol able to generate a synthetic catalog with an arbitrary large number of events. The numerical data reproduce the hierarchical organization in time and magnitude of experimental interevent time distribution.     

Large molecules reveal a linear length scaling for double photoionization

We have measured the ratio of doubly to singly charged parent ions of benzene, naphthalene, anthracene, and pentacene using monochromatized synchrotron radiation up to 30 eV above the corresponding threshold. Our measurements show a striking similarity between the ratio of doubly charged to all parent ions and the ratio for helium. Moreover, the magnitudes of the ratios for these molecules scale linearly with their lengths with an amazing accuracy. A high ratio, i.e., a high relative double-photoionization probability, makes a molecule an important source of low-energy electrons that can promote radiation damage of biomolecules [B. Bouda?ffa et al., Science 287, 1658 (2000)].     

Fluctuations and scaling in models for particle aggregation

We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to diffuse up to ? steps. Therefore the second model incorporates more fluctuations than the first, but still less than usual (Full Diffusion) models of deposition and diffusion on a crystal surface. We study the time dependence of the average densities of atoms and islands and the island size distribution. The Sequential Diffusion model displays a nontrivial steady-state regime where the island density increases and the island size distribution obeys scaling, much in the same way as the standard Full Diffusion model for epitaxial growth. Our results also allow to gain insight into the role of different types of fluctuations.     

Crossover scaling behaviour of the quasi-one-dimensional n-vector models

Crossovers in the quasi-one-dimensional n-vector models are discussed by making new scaling hypotheses. Predictions regarding critical point shifts and amplitudes are made for one-to two- and three-dimensional crossovers for 1 ? n ? ∞. Many new scaling functions are obtained exactly and studied by series-expanding methods.     

Particles and scaling for lattice fields and Ising models

The conjectured inequality ⁽⁶⁾0 leads to the existence of _d ⁴ fields and the scaling (continuum) limit ford-dimensional Ising models. Assuming ⁽⁶⁾0 and Lorentz covariance of this construction, we show that ford6 these _d ⁴ fields are free fields unless the field strength renormalizationZ ^–1 diverges. Let be the bare charge and the lattice spacing. Under the same assumptions (⁽⁶⁾0, Lorentz covariance andd6) we show that if ^4–d is bounded as 0, thenZ ^–1 is bounded and the limit field is free.Supported in part by the National Science Foundation under Grant MPS 74-13252Supported in part by the National Science Foundation under Grant MPS 75-21212     

Accurate local approximations to the triples correlation energy: formulation,implementation and tests of 5th-order scaling models

Local models for the triples part of the MP4 or CCSD(T) energy are formulated in terms of atom-labelled functions to describe the occupied and virtual orbital spaces. These models retain triple substitutions in which at most one of the three orbital replacements involves a change of atom. This reduces the number of triple substitutions from scaling with the 6th power of molecule size to scaling with the 4th power, and reduces the computational cost from 7th order to 5th order. Non-locality in the triple substitutions is dominated by terms in which an electron is scattered twice, while the other two singly scattered electrons exhibit non-locality that is similar to that seen in double substitutions. Two non-iterative computational models are designed around this observation. The first, ionic2, allows for non-locality only in the doubly-scattered electron, and recovers around 95% of the triples correlation energy (in the large-molecule limit). The second, ionic*, also approximately accounts for the effect of simultaneous non-locality of the doubly-scattered electron and the singly scattered electrons, and recovers over 99% of the triples energy. The latter yields a maximum error of 0.23?kcal?mol^?1 and an RMS error of 0.05?kcal?mol^?1 in the MP4/6-31G* triples energies of 179 closed shell molecules from the G3 database. A one-parameter empirical local model is introduced which recovers typically 99.7% of the MP4 triples correlation energy, and reduces the maximum error to 0.03?kcal?mol^?1 and the RMS error to 0.01?kcal?mol^?1. An implementation of these models is described which manifests the 5th-order scaling of cost with molecule size, without requiring storage of the local triples or the vvvo integrals.