Rotational misalignment of two stacked honeycomb lattices produces a moire pattern that is observable in scanning tunneling microscopy as a small modulation of the apparent surface height. This is known from experiments on highly-oriented pyrolytic g
raphite. Here, we observe the combined effect of three-layer moire patterns in multilayer graphene grown on SiC ($000bar{1}$). Small-angle rotations between the first and third layer are shown to produce a double-moire pattern, resulting from the interference of moire patterns from the first three layers. These patterns are strongly affected by relative lattice strain between the layers. We model the moire patterns as a beat-period of the mismatched reciprocal lattice vectors and show how these patterns can be used to determine the relative strain between lattices, in analogy to strain measurement by optical moire interferometry.
We calculate the speed of sound $c_s$ in an ideal gas of resonances whose mass spectrum is assumed to have the Hagedorn form $rho(m) sim m^{-a}exp{bm}$, which leads to singular behavior at the critical temperature $T_c = 1/b$. With $a = 4$ the pressu
re and the energy density remain finite at $T_c$, while the specific heat diverges there. As a function of the temperature the corresponding speed of sound initially increases similarly to that of an ideal pion gas until near $T_c$ where the resonance effects dominate causing $c_s$ to vanish as $(T_c - T)^{1/4}$. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around $T_c$, the actual critical behavior in these models is no longer present.
