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We present a stability analysis of the 2D t-t' Hubbard model on a squarelattice for various values of the next-nearest-neighbor hopping t' and electronconcentration. Using the free energy expression, derived by means of the flowequations method, we have performed numerical calculation for the variousrepresentations under the point group C_{4\nu} in order to determine at whichtemperature symmetry broken phases become more favorable than the symmetricphase. A surprisingly large number of phases has been observed. Some of themhave an order parameter with many nodes in k-space. Commonly discussed types oforder found by us are antiferromagnetism, d_{x^2-y^2}-wave singletsuperconductivity, d-wave Pomeranchuk instability and flux phase. A fewinstabilities newly observed are a triplet analog of the flux phase, aparticle-hole instability of p-type symmetry in the triplet channel which givesrise to a phase of magnetic currents, an s*-magnetic phase, a g-wavePomeranchuk instability and the band splitting phase with p-wave character.Other weaker instabilities are found also. A comparison with experiments ismade.Comment: revised version according to the referee remark

Possible phases of the two-dimensional $ \mathsf {t{\text -}t'}$ Hubbard model