Stoner Transition at Finite Temperature in a 2D Isotropic Fermi Liquid

We present the results of a mean-field analysis of the temperature evolution of a ferromagnetic Stoner transition in a two-dimensional (2D) system with an isotropic dispersion $\varepsilon_k \propto k^{2\alpha}$, which for $\alpha >1$ models flat dispersions in various multi-layer graphene systems in a displacement field. This study is an extension to a finite $T$ of previous studies at $T=0$, which found both first-order and second-order Stoner transitions, depending on the value of $\alpha$ and special behavior at $\alpha =1$ and $\alpha =2$. We find that the Stoner transition at a finite $T$ displays new features not seen at $T=0$. The most interesting one is the reentrant behavior, where the ordered state emerges as temperature is increased. This behavior develops at $\alpha >1.4$ and the range where it holds increases with $\alpha$. We conjecture that the reentrant behavior is the fundamental feature of the Stoner transition in 2D, not sensitive to the details of the electronic structure.