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epsilon expansion for correlated percolation: applications to gels

A Coniglio and T C Lubensky

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The 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.


PACS

82.70.Gg Gels and sols

64.60.A- Specific approaches applied to studies of phase transitions

64.75.-g Phase equilibria

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

64.60.F- Equilibrium properties near critical points, critical exponents

MSC

82B27 Critical phenomena

82B26 Phase transitions (general)

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

82B28 Renormalization group methods (See also 81T17)

82B43 Percolation (See also 60K35)

Subjects

Soft matter, liquids and polymers

Condensed matter: structural, mechanical & thermal

Statistical physics and nonlinear systems

Chemical physics and physical chemistry

Dates

Issue 5 (1 May 1980)



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