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Abstract

We investigate a competition of tendencies toward ferromagnetic and incommensurate order in two-dimensional fermionic systems within functional renormalization-group technique, accounting for the self-energy corrections and using temperature as a scale parameter. We assume that the Fermi surface (FS) is substantially curved and lies in the vicinity of van Hove singularity points. It is shown that the character of magnetic fluctuations is strongly asymmetric with respect to the Fermi level position relative to van Hove singularity (VHS). For the Fermi level above VHS, we find at low temperatures dominant incommensurate magnetic fluctuations, while below the VHS level, we find indications for the ferromagnetic ground state. In agreement with the Mermin-Wagner theorem, at finite temperatures and in small magnetic fields, we obtain small magnetization, which appears to be a power-law function of magnetic field. It is found that the FS curvature is slightly increased by correlation effects, and the renormalized bandwidth decreases at sufficiently low temperatures.