The inclusion of a local measure term corresponding to
was studied by Brügmann and Marinari [56,
57,
58]. This amounts to adding to the action a term of the form
, where
o
(v) is the number of 4-simplices containing a vertex
v
. \ For
, this seems to lead merely to a shift of the critical line.
This setting has been revived recently by Renken [178,
177] in the context of a renormalization group analysis.