Thermal buckling transition in graphene : Static and dynamical critical exponents

We study numerically the thermal buckling transition in graphene membranes under compressive strain and clamped boundaries employing an atomistic quasiharmonic model. The numerical simulations combine three different Monte Carlo methods, local moves, collective wave moves and parallel tempering. We determine the static and the dynamical critical exponents by finite-size scaling, and the nonlinear response to a transverse force near the transition. The correlation length exponent and the nonlinear response are in good agreement with recent renormalization-group calculations of elastic membranes. Despite the applied strain, we find a dynamical critical exponent and diffusion exponent of height fluctuations at the transition close to the value for freestanding graphene, z=2(1+ζ) and α=ζ/(ζ+1), where ζ is the static roughening exponent, as obtained in a recent study with a phase-field crystal model.