Fractal Behavior of Tethered Networks

摘要: Tethered networks are large macromolecules with regular (D-dimensional) connectivity, embedded in a d-dimensional space. Such may exhibit variety of non-trivial fractal behaviors. A “Landau-Ginzburg” field theory is proposed to describe statistical mechanics such structures. Effective elasticity and rigidity terms emerge naturally as consequence while longer-range interactions also included. combined Mean-Field/Flory treatment reveals crumpled, rigid, compact phases. Fluctuations (as explored by various renormalization-group schemes) play crucial role determining the exponents each these phases, well at phase transitions.