  Electron instabilities in the Hubbard model with the next nearest neighbor
coupling are calculated by exact diagonalization in finite, two-dimensional
Betts cells (lattices). A viable spin and charge coherent pairing, signaled by
quantum critical points and a negative charge gap region, is found in 8- and
10-site Betts lattices at small and moderate U regions consistent with our
exact results in elementary bipartite geometries [Phys. Rev. B 78 (2008)
075431]. The contour isolines for continuous temperature driven-crossover
between the Mott-Hubbard insulating and coherent pairing phases are
demonstrated. The criteria for smooth and abrupt phase transitions are found
for systematic enhancement of coherent pairing by optimization of the next
nearest neighbor coupling parameter.
