Freezing of Triangulations

Zero temperature dynamics of two dimensional triangulations of a torus with curvature energy is described. Numerical simulations strongly suggest that the model get frozen in metastable states, made of topological defects on flat surfaces, that group into clusters of same topological charge. It is conjectured that freezing is related to high temperature structure of baby universes.Comment: 17 pages, 15 figures. 1 section added on connections between present work and inherent structures ideas; 1 paragraph added in the conclusion; 1 figure added; published versio

Nonperturbative renormalization group approach to Lifshitz critical behaviour

The behaviour of a d-dimensional vectorial N=3 model at a m-axial Lifshitz critical point is investigated by means of a nonperturbative renormalization group approach that is free of the huge technical difficulties that plague the perturbative approaches and limit their computations to the lowest orders. In particular being systematically improvable, our approach allows us to control the convergence of successive approximations and thus to get reliable physical quantities in d=3.Comment: 6 pages, 3 figure

Site Percolation on Planar Φ3\Phi^{3} Random Graphs

In this paper, site percolation on random $\Phi^{3}$ planar graphs is studied by Monte-Carlo numerical techniques. The method consists in randomly removing a fraction $q=1-p$ of vertices from graphs generated by Monte-Carlo simulations, where $p$ is the occupation probability. The resulting graphs are made of clusters of occupied sites. By measuring several properties of their distribution, it is shown that percolation occurs for an occupation probability above a percolation threshold $p_{c}$=0.7360(5). Moreover, critical exponents are compatible with those analytically known for bond percolation.Comment: 8 pages, 10 figures. Accepted in Phys. Rev. E ; published versio

A glassy phase in quenched disordered graphene and crystalline membranes

We investigate the flat phase of $D$-dimensional crystalline membranes embedded in a $d$-dimensional space and submitted to both metric and curvature quenched disorders using a nonperturbative renormalization group approach. We identify a second order phase transition controlled by a finite-temperature, finite-disorder fixed point unreachable within the leading order of $\epsilon=4-D$ and $1/d$ expansions. This critical point divides the flow diagram into two basins of attraction: that associated to the finite-temperature fixed point controlling the long distance behaviour of disorder-free membranes and that associated to the zero-temperature, finite-disorder fixed point. Our work thus strongly suggests the existence of a whole low-temperature glassy phase for quenched disordered graphene, graphene-like compounds and, more generally, crystalline membranes.Comment: 6 pages, 1 figur

Universal behaviors in the wrinkling transition of disordered membranes

The wrinkling transition experimentally identified by Mutz et al. [Phys. Rev. Lett. 67, 923 (1991)] and then thoroughly studied by Chaieb et al. [Phys. Rev. Lett. 96, 078101 (2006)] in partially polymerized lipid membranes is reconsidered. One shows that the features associated with this transition, notably the various scaling behaviors of the height-height correlation functions that have been observed, are qualitatively and quantitatively well described by a recent nonperturbative renormalization group (NPRG) approach to quenched disordered membranes by Coquand et al. [Phys. Rev E 97, 030102 (2018)]. As these behaviors are associated with fixed points of RG transformations they are universal and should also be observed in, e.g., defective graphene and graphene-like materials.Comment: 6 pages, 2 figures, published versio

Robustness of planar random graphs to targeted attacks

In this paper, robustness of planar trivalent random graphs to targeted attacks of highest connected nodes is investigated using numerical simulations. It is shown that these graphs are relatively robust. The nonrandom node removal process of targeted attacks is also investigated as a special case of non-uniform site percolation. Critical exponents are calculated by measuring various properties of the distribution of percolation clusters. They are found to be roughly compatible with critical exponents of uniform percolation on these graphs.Comment: 9 pages, 11 figures. Added references.Corrected typos. Paragraph added in section II and in the conclusion. Published versio

Towards a Non-Perturbative Renormalization of Euclidean Quantum Gravity

A real space renormalization group technique, based on the hierarchical baby-universe structure of a typical dynamically triangulated manifold, is used to study scaling properties of 2d and 4d lattice quantum gravity. In 4d, the $\beta$-function is defined and calculated numerically. An evidence for the existence of an ultraviolet stable fixed point of the theory is presentedComment: 12 pages Latex + 1 PS fi

A Topological Glass

We propose and study a model with glassy behavior. The state space of the model is given by all triangulations of a sphere with $n$ nodes, half of which are red and half are blue. Red nodes want to have 5 neighbors while blue ones want 7. Energies of nodes with different numbers of neighbors are supposed to be positive. The dynamics is that of flipping the diagonal of two adjacent triangles, with a temperature dependent probability. We show that this system has an approach to a steady state which is exponentially slow, and show that the stationary state is unordered. We also study the local energy landscape and show that it has the hierarchical structure known from spin glasses. Finally, we show that the evolution can be described as that of a rarefied gas with spontaneous generation of particles and annihilating collisions

Varied Signature Splitting Phenomena in Odd Proton Nuclei

Varied signature splitting phenomena in odd proton rare earth nuclei are investigated. Signature splitting as functions of $K$ and $j$ in the angular momentum projection theory is explicitly shown and compared with those of the particle rotor model. The observed deviations from these rules are due to the band mixings. The recently measured $^{169}$Ta high spin data are taken as a typical example where fruitful information about signature effects can be extracted. Six bands, two of which have not yet been observed, were calculated and discussed in detail in this paper. The experimentally unknown band head energies are given