  We present a stability analysis of the 2D t-t' Hubbard model on a square
lattice for various values of the next-nearest-neighbor hopping t' and electron
concentration. Using the free energy expression, derived by means of the flow
equations method, we have performed numerical calculation for the various
representations under the point group C_{4\nu} in order to determine at which
temperature symmetry broken phases become more favorable than the symmetric
phase. A surprisingly large number of phases has been observed. Some of them
have an order parameter with many nodes in k-space. Commonly discussed types of
order found by us are antiferromagnetism, d_{x^2-y^2}-wave singlet
superconductivity, d-wave Pomeranchuk instability and flux phase. A few
instabilities newly observed are a triplet analog of the flux phase, a
particle-hole instability of p-type symmetry in the triplet channel which gives
rise to a phase of magnetic currents, an s*-magnetic phase, a g-wave
Pomeranchuk instability and the band splitting phase with p-wave character.
Other weaker instabilities are found also. A comparison with experiments is
made.
