Low-temperature conformational transition of a square-lattice polymer

We study the low-temperature transition of polymers with attractive nearest-neighbor interactions on a square lattice. Measuring the specific heat obtained by using the exact number of possible conformations for each energy value, we find a peak in the low-temperature region, distinct from the peak corresponding to the coil-globule transition. We find that the low-temperature peak becomes prominent for specific polymer lengths called the magic lengths, for which the ground state forms a square or a rectangle. The low-temperature peaks for magic lengths are more intense than those for other lengths and appear at lower temperatures.