Collapse transition of a square-lattice polymer with next   nearest-neighbor interaction
  We study the collapse transition of a polymer on a square lattice with both nearest-neighbor and next nearest-neighbor interactions, by calculating the exact partition function zeros up to chain length 36. The transition behavior is much more pronounced than that of the model with nearest-neighbor interactions only. The crossover exponent and the transition temperature are estimated from the scaling behavior of the first zeros with increasing chain length. The results suggest that the model is of the same universality class as the usual theta point described by the model with only nearest-neighbor interaction. 
Jae Hwan Lee, Seung-Yeon Kim, and Julian Lee
cond-mat.stat-mech