Thermal buckling and symmetry breaking in thin ribbons under compression

Understanding thin sheets, ranging from the macro to nanoscale, can allow control of mechanical properties such as deformability. Out-of-plane buckling due in-plane compression be a key feature in designing new materials. While thin-plate theory predict critical thresholds for frames and nanoribbons at very low temperatures, unifying framework describe effects thermal fluctuations on more elevated temperatures presents subtle difficulties. We develop test theoretical approach that includes both an out-of-plane perturbing field mechanics thermalised ribbons above below transition. show that, once elastic constants are renormalised take into account ribbon’s width (in units length scale), we map physics onto mean-field treatment buckling, provided is short compared ribbon persistence length. Our predictions checked by extensive molecular dynamics simulations under axial compression.