Fractal dimension and degree of order in sequential deposition of mixture

We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . We explicitly obtain the scaling function in the case of random sequential adsorption (RSA) and show that the pattern created in the long time limit becomes scale invariant. This pattern can be described by an unique exponent, the fractal dimension. In addition, we introduce an external tuning parameter beta to describe the correlated sequential deposition of a mixture of particles where the degree of correlation is determined by beta, while beta=0 corresponds to random sequential deposition of mixture. We show that the fractal dimension of the resulting pattern increases as beta increases and reaches a constant non-zero value in the limit $\beta \to \infty$ when the pattern becomes perfectly ordered or non-random fractals.Comment: 16 pages Latex, Submitted to Phys. Rev.

Universality of low-energy scattering in (2+1) dimensions

We prove that, in (2+1) dimensions, the S-wave phase shift, $\delta_0(k)$, k being the c.m. momentum, vanishes as either $\delta_0 \to {c\over \ln (k/m)} or \delta_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=\pi/2$. This result is established first in the framework of the Schr\"odinger equation for a large class of potentials, second for a massive field theory from proved analyticity and unitarity, and, finally, we look at perturbation theory in $\phi_3^4$ and study its relation to our non-perturbative result. The remarkable fact here is that in n-th order the perturbative amplitude diverges like $(\ln k)^n$ as $k\to 0$, while the full amplitude vanishes as $(\ln k)^{-1}$. We show how these two facts can be reconciled.Comment: 23 pages, Late

Z_3 Quantum Criticality in a spin-1/2 chain model

The stability of the magnetization $m=1/3$ plateau phase of the XXZ spin-1/2 Heisenberg chain with competing interactions is investigated upon switching on a staggered transverse magnetic field. Within a bosonization approach, it is shown that the low-energy properties of the model are described by an effective two-dimensional XY model in a three-fold symmetry-breaking field. A phase transition in the three-state Potts universality class is expected separating the $m=1/3$ plateau phase to a phase where the spins are polarized along the staggered magnetic field. The Z$_3$ critical properties of the transition are determined within the bosonization approach.Comment: 5 pages, revised versio

Polydisperse Adsorption: Pattern Formation Kinetics, Fractal Properties, and Transition to Order

We investigate the process of random sequential adsorption of polydisperse particles whose size distribution exhibits a power-law dependence in the small size limit, $P(R)\sim R^{\alpha-1}$. We reveal a relation between pattern formation kinetics and structural properties of arising patterns. We propose a mean-field theory which provides a fair description for sufficiently small $\alpha$. When $\alpha \to \infty$, highly ordered structures locally identical to the Apollonian packing are formed. We introduce a quantitative criterion of the regularity of the pattern formation process. When $\alpha \gg 1$, a sharp transition from irregular to regular pattern formation regime is found to occur near the jamming coverage of standard random sequential adsorption with monodisperse size distribution.Comment: 8 pages, LaTeX, 5 figures, to appear in Phys.Rev.

A strong-coupling analysis of two-dimensional O(N) sigma models with N≥3N\geq 3 on square, triangular and honeycomb lattices

Recently-generated long strong-coupling series for the two-point Green's functions of asymptotically free ${\rm O}(N)$ lattice $\sigma$ models are analyzed, focusing on the evaluation of dimensionless renormalization-group invariant ratios of physical quantities and applying resummation techniques to series in the inverse temperature $\beta$ and in the energy $E$. Square, triangular, and honeycomb lattices are considered, as a test of universality and in order to estimate systematic errors. Large-$N$ solutions are carefully studied in order to establish benchmarks for series coefficients and resummations. Scaling and universality are verified. All invariant ratios related to the large-distance properties of the two-point functions vary monotonically with $N$, departing from their large-$N$ values only by a few per mille even down to $N=3$.Comment: 53 pages (incl. 5 figures), tar/gzip/uuencode, REVTEX + psfi

Critical properties of Ising model on Sierpinski fractals. A finite size scaling analysis approach

The present paper focuses on the order-disorder transition of an Ising model on a self-similar lattice. We present a detailed numerical study, based on the Monte Carlo method in conjunction with the finite size scaling method, of the critical properties of the Ising model on some two dimensional deterministic fractal lattices with different Hausdorff dimensions. Those with finite ramification order do not display ordered phases at any finite temperature, whereas the lattices with infinite connectivity show genuine critical behavior. In particular we considered two Sierpinski carpets constructed using different generators and characterized by Hausdorff dimensions d_H=log 8/log 3 = 1.8927.. and d_H=log 12/log 4 = 1.7924.., respectively. The data show in a clear way the existence of an order-disorder transition at finite temperature in both Sierpinski carpets. By performing several Monte Carlo simulations at different temperatures and on lattices of increasing size in conjunction with a finite size scaling analysis, we were able to determine numerically the critical exponents in each case and to provide an estimate of their errors. Finally we considered the hyperscaling relation and found indications that it holds, if one assumes that the relevant dimension in this case is the Hausdorff dimension of the lattice.Comment: 21 pages, 7 figures; a new section has been added with results for a second fractal; there are other minor change

Long-term trends of land use and demography in Greece: a comparative study

This paper offers a comparative study of land use and demographic development in northern and southern Greece from the Neolithic to the Byzantine period. Results from summed probability densities (SPD) of archaeological radiocarbon dates and settlement numbers derived from archaeological site surveys are combined with results from cluster-based analysis of published pollen core assemblages to offer an integrated view of human pressure on the Greek landscape through time. We demonstrate that SPDs offer a useful approach to outline differences between regions and a useful complement to archaeological site surveys, evaluated here especially for the onset of the Neolithic and for the Final Neolithic (FN)/Early Bronze Age (EBA) transition. Pollen analysis highlight differences in vegetation between the two sub-regions, but also several parallel changes. The comparison of land cover dynamics between two sub-regions of Greece further demonstrates the significance of the bioclimatic conditions of core locations and that apparent oppositions between regions may in fact be two sides of the same coin in terms of socio-ecological trajectories. We also assess the balance between anthropogenic and climate-related impacts on vegetation and suggest that climatic variability was as an important factor for vegetation regrowth. Finally, our evidence suggests that the impact of humans on land cover is amplified from the Late Bronze Age (LBA) onwards as more extensive herding and agricultural practices are introduced.Domesticated Landscapes of the Peloponnese (DoLP

Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy

We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these models with N-color Ashkin-Teller models, discrete cubic models, planar model with fourth order anisotropy, and structural phase transition in adsorbed monolayers are discussed. Our results for N=2 (XY model with cubic anisotropy) are compatible with the existence of a line of fixed points joining the Ising and the O(2) fixed points. Along this line the exponent $\eta$ has the constant value 1/4, while the exponent $\nu$ runs in a continuous and monotonic way from 1 to $\infty$ (from Ising to O(2)). For N\geq 3 we find a cubic fixed point in the region $u, v \geq 0$, which is marginally stable or unstable according to the sign of the perturbation. For the physical relevant case of N=3 we find the exponents $\eta=0.17(8)$ and $\nu=1.3(3)$ at the cubic transition.Comment: 14 pages, 9 figure