Collapse of branched polymers

Abstract

Exact calculations using transfer matrices on finite strips are performed to study the two-dimensional problem of one lattice animal with an attractive nearest neighbour interaction. Thermodynamic quantities such as specific heat, compressibility, thermal expansion are calculated. Finite size scaling with two strips of different widths yields very accurate approximations of the critical line. Using three different strip widths or the two largest eigenvalues of the transfer matrix, we present two ways of obtaining the tricritical point and its exponents. Our estimations are quite stable when we increase the strip width and we can give rather accurate predictions. Lastly our model can also be interpreted as a gel whose parameters are temperature and pressure showing the experimentally known phenomenon of the collapse.