Universal behaviors in the wrinkling transition of disordered membranes.

The wrinkling transition experimentally identified by Mutz et al. [Phys. Rev. Lett. 67, 923 (1991)PRLTAO0031-900710.1103/PhysRevLett.67.923] and then thoroughly studied by Chaieb et al. [Phys. Rev. Lett. 96, 078101 (2006)]PRLTAO0031-900710.1103/PhysRevLett.96.078101 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 approach to quenched disordered membranes by Coquand et al. [Phys. Rev E 97, 030102(R) (2018)]2470-004510.1103/PhysRevE.97.030102. As these behaviors are associated with fixed points of renormalization group transformations they are universal and should also be observed in, e.g., defective graphene and graphene-like materials.

Glassy phase in quenched disordered 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 ε=4-D and 1/d expansions. This critical point divides the flow diagram into two basins of attraction: that associated with the finite-temperature fixed point controlling the long-distance behavior of disorder-free membranes and that associated with the zero-temperature, finite-disorder fixed point. Our work thus strongly suggests the existence of a whole low-temperature glassy phase for quenched disordered crystalline membranes and, possibly, for graphene and graphene-like compounds.

First-order phase transitions in polymerized phantom membranes.

The crumpled-to-flat phase transition that occurs in D-dimensional polymerized phantom membranes embedded in a d-dimensional space is investigated nonperturbatively using a field expansion up to order 8 in powers of the order parameter. We get the critical dimension dcr(D) that separates a second-order region from a first-order one everywhere between D=4 and 2. Our approach strongly suggests that the phase transitions that take place in physical membranes are of first order in agreement with most recent numerical simulations.

Crumpled-to-tubule transition in anisotropic polymerized membranes: beyond the ϵ expansion.

Anisotropic D-dimensional polymerized phantom membranes are investigated within a nonperturbative renormalization group framework. One focuses on the transition between a high-temperature, crumpled phase and a low-temperature, tubular phase where the membrane is flat along one direction and crumpled along the other ones. While the upper critical dimension--D(uc)=5/2--is close to D=2, the weak-coupling perturbative approach is qualitatively and quantitatively wrong. We show that our approach is free of the problems encountered within the perturbative framework and provides physically meaningful critical quantities.

Crumpling transition and flat phase of polymerized phantom membranes.

Polymerized phantom membranes are revisited using a nonperturbative renormalization-group approach. This allows one to investigate both the crumpling transition and the low-temperature flat phase in any internal dimension D and embedding dimension d and to determine the lower critical dimension. The crumpling phase transition for physical membranes is found to be of second order within our approximation. A weak first-order behavior, as observed in recent Monte Carlo simulations, is however not excluded.

Site percolation on planar 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.