Phase transition of surface models with intrinsic curvature
  It is reported that a surface model of Polyakov strings undergoes a first-order phase transition between smooth and crumpled (or branched polymer) phases. The Hamiltonian of the model contains the Gaussian term and a deficit angle term corresponding to the weight of the integration measure dX in the partition function. 
H. Koibuchi, N. Kusano, A. Nidaira, Z. Sasaki, and K. Suzuki