| Abstract |
In this talk, we introduce a two-dimensional semiflexible membrane model whose Hamiltonian is given by $H[\phi]=\sum_x |\nabla \phi_x|^2 +N^\lambda |\Delta \phi_x|^2$, interpolating between the discrete Gaussian free field (DGFF) and the membrane model (MM).
We analyze its infinite-volume behavior and identify distinct regimes depending on the parameter $\lambda$. If $\lambda<0$, the covariance behaves similarly to that of the DGFF, while for $\lambda>2$, it resembles a rescaled MM. In the intermediate regime $0\le \lambda\le 2$, we observe a qualitatively different behavior: a nontrivial dependence on the distance between points. We further determine the leading order constant of the covariance.
These results provide a unified description of the crossover from gradient-dominated to curvature-dominated behavior in this class of models. |
