Glassy phase in quenched disordered crystalline membranes

Abstract

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.

Universal behaviors in the wrinkling transition of disordered membranes

“…The conclusion of our work is fourfold. First, we have shown that the longstanding problem of the wrinkling transition taking place in partially polymerized lipid membranes is both qualitatively and quantitatively clarified by means of the NPRG approach used in [3]. Second, reciprocally, this agreement validates the NPRG approach to disordered polymerized and, in particular, consolidates the prediction of the existence of three nontrivial fixed points in the RG flow of the model (1), in contradiction with all previous works.…”

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The wrinkling transition experimentally identified by Mutz et al[1] and then thoroughly studied by Chaieb et al [2] 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 [3]. 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.

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“…At the fully attractive, vanishing-T , finite-disorder fixed point P 5 it has been found [3] that η 5 = 0.449 and η 5 = 0.277. This in contrast with both [57,58] and [39] where η 5 = η 5 so that P 5 was found to correspond to a marginal -in fact marginally unstable -fixed point.…”

“…This in contrast with both [57,58] and [39] where η 5 = η 5 so that P 5 was found to correspond to a marginal -in fact marginally unstable -fixed point. Using the data of [3] one finds a roughness exponent given by ζ 5 = 0.86 that, according to (4) and the scaling laws of χ(q) and C(q), controls the long-distance behavior of the height-height correlation function G hh (q). This corresponds to a power exponent γ 5 = 2.72.…”

“…Note that such a value would correspond to the expected value for a fluid membrane, which could be a hint that below φ = 10%, partially polymerized lipid membranes do not behave as polymerized membranes anymore. At the stable, finite-T , finite-disorder fixed point P 4 , it has been found by NPRG in [3] that η 4 = 2η 4 = 0.85 (see [8] for a review of other approaches) that corresponds to ζ 4 = 0.575 and γ 4 = 2.15. As seen on Fig.2 this is again in good agreement with the results found in [2] at high polymerization with a value of γ that saturates at 2.…”