Self-similar approximations for thermodynamic potentials

The method of self-similar approximation is extended here to the problem of calculating thermodynamic potentials in statistical mechanics. To formulate an optimal scheme of the method, we compare its different variants connected with different definitions of governing functions and damping parameters. Stability conditions are analyzed. All concions are made apparent by calculating the free energy of a zero-dimensional ϕ4 model. The optimal variant of the method is shown to be stable providing a good accuracy in the whole range of a coupling parameter, from zero up to infinity.