  An effective model in the isolated dimer limit of the Kitaev-type model on a
decorated honeycomb lattice is investigated at finite temperature. The ground
state of this model is exactly shown to be a chiral spin liquid with
spontaneous breaking of time reversal symmetry. We elaborate the
finite-temperature phase diagram by using the mean-field approximation and
Monte Carlo simulation. We find that the phase transition between the
high-temperature paramagnetic phase and the low-temperature chiral spin liquid
phase is always of second order in the Monte Carlo results, although a
tricritical point appears in the mean-field phase diagram. The finite-size
scaling analysis of the Monte Carlo data indicates that the phase transition
belongs to the two-dimensional Ising universality class.
