# Statistics of randomly branched polymers in a semi-space

### M. V. Tamm 1, 2, S. K. Nechaev 2, 3, I. Ya. Erukhimovich 1, 4

#### European Physical Journal E 17 (2005) 209-219

We investigate the statistical properties of a randomly branched 3--functional $N$--link polymer chain without excluded volume, whose one point is fixed at the distance $d$ from the impenetrable surface in a 3--dimensional space. Exactly solving the Dyson-type equation for the partition function $Z(N,d)=N^{-\\theta} e^{\\gamma N}$ in 3D, we find the \'surface\' critical exponent $\\theta={5/2}$, as well as the density profiles of 3--functional units and of dead ends. Our approach enables to compute also the pairwise correlation function of a randomly branched polymer in a 3D semi-space.

• 1. Physics Department,
Moscow State University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Landau Institute for Theoretical Physics,
Landau Institute for Theoretical Physics
• 4. A.N. Nesmeyanov Institute of Organoelement Coumpounds RAS,
A.N. newmeyanov Institute of Organoelement Coumpounds RAS