Triangular Lattice Foldings–a Transfer Matrix Study

Connection between discrete and continuum models of polymerized (tethered) surfaces has been investigated by applying a transfer matrix method to a discrete rigid-bond triangular lattice, which is allowed to fold on itself along its bonds in a two-dimensional embedding space. As its continuum counterpart, the model has an extensive entropy and the mean squared distance between two sites of a folded lattice increases logarithmically with the linear distance between the sites in the unfolded state. The model lattice with bending rigidity remains unfolded at any finite temperature, unlike real polymerized surfaces.