  We study the two-dimensional Ising model on a network with a novel type of
quenched topological (connectivity) disorder. We construct random lattices of
constant coordination number and perform large scale Monte Carlo simulations in
order to obtain critical exponents using finite-size scaling relations. We find
disorder-dependent effective critical exponents, similar to diluted models,
showing thus no clear universal behavior. Considering the very recent results
for the two-dimensional Ising model on proximity graphs and the coordination
number correlation analysis suggested by Barghathi and Vojta (2014), our
results indicate that the planarity and connectedness of the lattice play an
important role on deciding whether the phase transition is stable against
quenched topological disorder.
