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 ${\mathit{q}}_{\mathrm{\perp }}^{\mathrm{\eta }}$, while the membrane bend modulus κ diverges like ${\mathit{q}}^{\mathrm{-}\mathrm{\eta }}$, with ${\mathrm{\eta }}_{\mathrm{\perp }}$+1/2(5-D)η=5-2D, exactly. The 5/2-ɛ expansion predicts η=0.27±0.03 and ${\mathrm{\eta }}_{\mathrm{\perp }}$=0.60±0.05 in D=2. We discuss several experiments to measure these exponents.