Ising-like transitions and anomalous thermal expansion in fluctuating membranes with puckered impurity arrays

Idealized homogeneous membranes and membranes with various types of defects have been studied for the last thirty years. However, finite temperature investigations of membranes with a periodic array of impurities that can buckle on either side of the membrane are less common. In this work, we present molecular dynamics simulations of elastic membranes with dilational impurities arranged in a square lattice. The staggered "magnetization" of the up-down buckled impurities acts as the order parameter for a 2D Ising phase transition of the puckers in the flat phase. We find that both that the ground state and the finite temperature behavior of this system can be described as a highly compressible antiferromagnetic Ising model. Non-trivial couplings between dilations and both flexural and in-plane phonons alter the long-wavelength physics, resulting in anomalous thermal expansion. The isothermal expansion picks up a diverging specific heat singularity because the buckled puckers no longer pack efficiently as the order-disorder transition progresses.