Ideal chains with fixed self-intersection rate

Abstract: We consider ideal chains in a hypercubic lattice \mathbb{Z}^{d}, d\geq3, with a fixed ratio m of self-intersection per monomer. Despite the simplicity of the geometrical constraint, this model shows some interesting properties, such as a collapse transition for a critical value m_{c}. Numerical simulations show a Self-Avoiding-Walk-like behavior for m<m_{c}, and a compact cluster configuration for m>m_{c}. The collapse seems to show the same characteristics as the canonical thermodynamical models for the coil-globule transition.