Asymptotic freedom at zero temperature in free-standing crystalline membranes
We investigate the effects of quantum (zero-temperature) long-wavelength fluctuations of free-standing crystalline membranes, which are two-dimensional objects embedded into three-dimensional space. The fluctuations produce logarithmic renormalization of elasticity and bending moduli of the membranes. We find one-loop RG equations to demonstrate that the system is in the “asymptotic freedom” regime; that is, the quantum
fluctuations destabilize the flat membrane phase.