The Euler buckling of rods is a long-studied mechanical instability, and it remains relevant to this day, as the constituent components in many biological and physical systems are linear polymers, such as microtubules or carbon nanotubes. At finite temperature, if a polymer is shorter than its persistence length, then the polymer is semiflexible, and its elasticity remains rodlike. But polymers can also stretch due to their finite extensibility, which can couple to energetically cheap bending deformations in nonlinear ways when a load is applied to the system. We show how the interplay between thermal fluctuations and nonlinear elasticity dramatically modifies the Euler buckling instability for compressed semiflexible polymers in a fixed strain ensemble. We identify a Ginzburg-like length scale beyond which thermally excited undulations lead to a softened Young's modulus, while the polymer nevertheless remains semiflexible. Both perturbative calculations and numerical Monte Carlo simulations suggest a qualitative change in several scaling properties of the buckling transition. The critical compressional strain for thermal buckling now increases with system size, in contrast to athermal buckling, where it decreases with system size. Renormalization group calculations confirm this picture, and also show that thermal buckling is controlled by a new fixed point with different critical exponents compared to classical Euler buckling.

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• Classical statistical mechanics
• Critical phenomena
• Mechanical deformation
• Polymer behavior