The collapse transition of linear polymers on fractal lattices

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Abstract
The authors show that for linear polymers a collapse transition exists on several fractal lattices and obtain exact results for the critical exponents at this transition. A 'rod-like' phase is found in some cases at intermediate temperatures, between the swollen phase and the collapsed phase. They introduce infinitesimal recursion relations with correlation function rescaling as the formal limit of a class of fractals, which give a better approximation to Euclidean 2D lattices. The gyration radius exponent at the transition temperature lies in the range nu 1=0.546+or-0.010, in good agreement with a recent transfer matrix calculation. The possible relevance of anisotropy at the collapse transition is discussed.