Pomeranchuk and other instabilities in thet−t′Hubbard model at the Van Hove filling

We present a stability analysis of the two-dimensional $t-t^{\prime }$ Hubbard model for various values of the next-nearest-neighbor hopping $t^{\prime },$ and electron concentrations close to the Van Hove filling by means of the flow equation method. For $t^{\prime }>~-t/3\mathrm{}$ a $d_{x^2-y^2}$-wave Pomeranchuk instability dominates (apart from antiferromagnetism at small $t^{\prime }).\mathrm{}$ At $t^{\prime }<-t/3,$ the leading instabilities are a g-wave Pomeranchuk instability and p-wave particle-hole instability in the triplet channel at temperatures $T<\mathrm{}0.15t,$ and an $s^{*}$-magnetic phase for $T>\mathrm{}0.15t;$ upon increasing the electron concentration, the triplet analog of the flux phase occurs at low temperatures. Other weaker instabilities are also found.