On the Stability of a Spherically Symmetric Solution for a Two-Dimensional Magnet

One of the scenarios of high-temperature superconductivity is based on spin-polar pairing. The theory of the spin polaron is based on the properties of a 2D magnet. A common algorithm for investigating these properties is a spherically symmetric approach that preserves the constraints of exact theorems. The present paper provides a concise overview of some of the outcomes of the spherical approach with a focus on the stability of a self-consistent solution. The last section presents a model that does not allow for a stable solution, and discusses possible ways to overcome the problem.