Creasing of flexible membranes at vanishing tension

The properties of freestanding tensionless interfaces and membranes at low bending rigidity $\ensuremath{\kappa}$ are dominated by strong fluctuations self-avoidance thus outside the range standard perturbative analysis. We analyze this regime a simple discretized, self-avoiding membrane model on frame subject to periodic boundary conditions use Monte Carlo simulation dynamically triangulated surface techniques. find that rigidities, fall into three regimes: Below collapse transition ${\ensuremath{\kappa}}_{\mathrm{BP}}$ it is branched polymer instability where framed not defined, in below threshold ${\ensuremath{\kappa}}_{c}$ conformational correlation function characterized power-law behavior with continuously varying exponent $\ensuremath{\alpha}, 2<\ensuremath{\alpha}\ensuremath{\le}4$ above ${\ensuremath{\kappa}}_{c}, \ensuremath{\alpha}=4$ characteristic for linearized excitations. Response functions specific heat area compressibility display pronounced peaks close ${\ensuremath{\kappa}}_{c}$. results may be important description soft interface systems, such as microemulsions in-plane cooperative phenomena.