Pomeranchuk and other Instabilities in the t-t' Hubbard model at the Van Hove Filling

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We present a stability analysis of the two-dimensional t-t' Hubbard model for various values of the next-nearest-neighbor hopping t', and electron concentrations close to the Van Hove filling by means of the flow equation method. For t' > -t/3 a dₓ₂₋y₂-wave Pomeranchuk instability dominates (apart from antiferromagnetism at small t'). At t' < -t/3 the leading instabilities are a g-wave Pomeranchuk instability and p-wave particle-hole instability in the triplet channel at temperatures T < 0.15t, and an s*-magnetic phase for T > 0.15t; upon increasing the electron concentration the triplet analog of the flux phase occurs at low temperatures. Other weaker instabilities are found also.