A Coniglio and T C Lubensky 1980 J. Phys. A: Math. Gen. 13 1783 doi:10.1088/0305-4470/13/5/036
A Coniglio and T C Lubensky
Show affiliationsThe momentum space renormalisation group is applied to a Hamiltonian which describes site-bond correlated percolation, which in turn models the sol-gel transition when solvent effects are present. Mean field theory is used to determine the qualitative features of the phase diagram which includes sol and gel phases in either one- or two-phase regions. Recursion relations in d=6- epsilon dimensions are derived and are shown to have a fixed point corresponding to simultaneous gelation and phase separation. At this fixed point, the critical exponents describing phase separation are the same as for the Ising model nu 0=1/2, eta =0 for d>4 whereas those describing gelation differ from those for the usual percolation problem: nu 1=2/(d-2), eta 1=0 for 4<d<6.
64.60.A- Specific approaches applied to studies of phase transitions
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
64.60.F- Equilibrium properties near critical points, critical exponents
82B26 Phase transitions (general)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Soft matter, liquids and polymers
Condensed matter: structural, mechanical & thermal
Issue 5 (1 May 1980)
A Coniglio and T C Lubensky 1980 J. Phys. A: Math. Gen. 13 1783
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