  We investigate the Hubbard model on the triangular lattice at half-filling
using the dynamical cluster approximation (DCA) and dual fermion (DF) methods
in combination with continuous-time quantum Monte carlo (CT QMC) and
semiclassical approximation (SCA) methods. We study the one-particle properties
and nearest-neighbor spin correlations using the DCA method. We calculate the
spectral functions using the CT QMC and SCA methods. The spectral function in
the SCA and obtained by analytic continuation of the Pade approximation in CT
QMC are in good agreement. We determine the metal-insulator transition (MIT)
and the hysteresis associated with a first-order transition in the double
occupancy and nearest-neighbor spin correlation functions as a function of
temperature. As a further check, we employ the DF method and discuss the
advantages and limitation of the dynamical mean field theory (DMFT), DCA and
recently developed DF methods by comparing Green's functions. We find an
enhancement of antiferromagnetic (AF) correlations and provide evidence for
magnetically ordered phases by calculating the spin susceptibility.
