ABSTRACT
The theory of phase transitions is certainly one of the most interesting areas of statistical physics. in the language of the Legendre transform Γ the problem of determining the averages α and W(x) is a variational problem: it is necessary to find the stationarity point of the function Φ(α x) and the value of the function at this point. The transformation to a variational problem allows the natural introduction of such concepts as degeneracy (nonuniqueness) of a solution and spontaneous symmetry breaking. The classical and quantum Heisenberg ferromagnets differ from the Ising ferromagnet only in that the reduced external field and its conjugate variable, the magnetization, become three-vectors, and the invariance under change of sign of these quantities becomes invariance under rotations of the corresponding vectors (for isotropic exchange interaction of the spins). The chapter also discusses the infinite-volume limit or, as it is often called, the thermodynamical limit.
