arXiv subjects

O. Golinelli

Publications and source records attributed to O. Golinelli.

27 records · Page 2Linked to original sources

arXiv1997

Asymptotic behavior of two-terminal series-parallel networks

This paper discusses the enumeration of two-terminal series-parallel networks, i.e. the number of electrical networks built with n identical elements connected in series or parallel with two-terminal nodes. They frequently occur in applied probability theory as a model for real networks. The number of networks grows asymptotically like R^n/n^alpha, as for some models of statistical physics like self-avoiding walks, lattice animals, meanders, etc. By using a exact recurrence relation, the entropy is numerically estimated at R = 3.5608393095389433(1), and we show that the sub-leading universal exponent alpha is 3/2.

cond-mat.stat-mech↗

arXiv1997

Percolation Transition in the random antiferromagnetic spin-1 chain

We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet phase. We study the statistical properties of the percolation clusters by numerical simulations, and we compute exact exponents characterizing the transition by a real-space renormalization group calculation.

cond-mat.str-el↗

arXiv1996

Meanders: A Direct Enumeration Approach

We study the statistics of semi-meanders, i.e. configurations of a set of roads crossing a river through n bridges, and possibly winding around its source, as a toy model for compact folding of polymers. By analyzing the results of a direct enumeration up to n=29, we perform on the one hand a large n extrapolation and on the other hand we reformulate the available data into a large q expansion, where q is a weight attached to each road. We predict a transition at q=2 between a low-q regime with irrelevant winding, and a large-q regime with relevant winding.

hep-th↗

arXiv1996

Meanders and the Temperley-Lieb algebra

The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight $q$ per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram determinant as a function of $q$, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks.

hep-th↗

arXiv1995

Meander, Folding and Arch Statistics

The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular emphasis on three points: (i) the use of a direct recursive relation for building (semi) meanders (ii) the equivalence with a random matrix model (iii) the exact solution of simpler related problems, such as arch configurations or irreducible meanders.

hep-th↗

arXiv1995

Three-dimensional Folding of the Triangular Lattice

We study the folding of the regular triangular lattice in three dimensional embedding space, a model for the crumpling of polymerised membranes. We consider a discrete model, where folds are either planar or form the angles of a regular octahedron. These "octahedral" folding rules correspond simply to a discretisation of the 3d embedding space as a Face Centred Cubic lattice. The model is shown to be equivalent to a 96--vertex model on the triangular lattice. The folding entropy per triangle ${\rm ln} q_{3d}$ is evaluated numerically to be $q_{3d}=1.43(1)$. Various exact bounds on $q_{3d}$ are derived.

cond-mat↗

arXiv1994

Finite-lattice extrapolations for a Haldane gap antiferromagnet

We present results of exact diagonalizations of the isotropic antiferromagnetic S=1 Heisenberg chain by the Lanczos method, for finite rings of up to N=22 sites. The Haldane gap G(N) and the ground state energy per site e(N) converge, with increasing N, faster than a power law. By VBS and Shanks transformations, the extrapolated values are G=0.41049(2) and e=-1.401485(2). The spin-spin correlation function is well fit by exp(-r/xi)/sqrt(r) with xi=6.2.

cond-mat↗

arXiv1993

Magnetic Field Behaviour of a Haldane Gap Antiferromagnet

We investigate the magnetic field behaviour of an antiferromagnetic Heisenberg spin-1 chain with the most general single-ion anisotropy. We discuss the regime in which the magnetic field is below the transition value. The splitting of the Haldane triplet is obtained as a function of a field applied in an arbitrary orientation by means of a Lancz\H os exact diagonalization of chains of up to 16 spins. Our results are nicely summarized in terms of a first-order perturbation theory. We explain various level crossings that occur by the existence of discrete symmetries. A discussion is given of the electron spin resonance and neutron scattering experiments on the compound Ni(C$_2$H$_8$N$_2$)$_2$NO$_2$ClO$_4$ (NENP).

cond-mat↗

arXiv1992

Dynamical Properties of a Haldane Gap Antiferromagnet

We study the dynamic spin correlation function of a spin one antiferromagnetic chain with easy-plane single-ion anisotropy. We use exact diagonalization by the Lancz\H os method for chains of lengths up to N=16 spins. We show that a single-mode approximation is an excellent description of the dynamical properties. A variational calculation allows us to clarify the nature of the excitations. The existence of a two-particle continuum near zero wavevector is clearly seen both in finite-size effects and in the dynamical structure factor. The recent neutron scattering experiments on the quasi-one-dimensional antiferromagnet NENP are fully explained by our results.

cond-mat↗