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The systematic effective Lagrangian method was first formulated in thecontext of the strong interaction: chiral perturbation theory (CHPT) is theeffective theory of Quantum Chromodynamics (QCD). It was then pointed out thatthe method can be transferred to the nonrelativistic domain -- in particular,to describe the low-energy properties of ferromagnets. Interestingly, whereasfor Lorentz-invariant systems the effective Lagrangian method fails in onespatial dimension ($d_s$=1), it perfectly works for nonrelativistic systems in$d_s$=1. In the present brief review, we give an outline of the method and thenfocus on the partition function for ferromagnetic spin chains, ferromagneticfilms and ferromagnetic crystals up to three loops in the perturbativeexpansion -- an accuracy never achieved by conventional condensed mattermethods. We then compare ferromagnets in $d_s$=1,2,3 with the behavior of QCDat low temperatures by considering the pressure and the order parameter. Thetwo apparently very different systems (ferromagnets and QCD) are related from auniversal point of view based on the spontaneously broken symmetry. In eithercase, the low-energy dynamics is described by an effective theory containingGoldstone bosons as basic degrees of freedom.

Partition Function in One, Two and Three Spatial Dimensions from Effective Lagrangian Field Theory