Anomalous elasticity and symmetry breaking fields in tethered membranes

We study the eleasticity of tethered, crystalline membranes in an applied in-plane electric field. The field lowers the critical dimension for the onset of anomalous elasticity from 4 to 5/2, allowing stringent experimental tests of the predictions of the renormalization group to be made. Two-in-plane elastic constants vanish at small wave vectors q like q, while the membrane bend modulus diverges like q-, with +1/2(5-D)=5-2D, exactly. The 5/2-expansion predicts =0.270.03 and =0.600.05 in D=2. We discuss several experiments to measure these exponents. © 1992 The American Physical Society.