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We study the variational problem as described by Balaban in hisrenormalization group method for Yang-Mills theories in $d= 3, 4$ and adapt itto a class of Non-Linear Sigma Models in $d=2$. The result of the variationalproblem is a minimal configuration which can serve as a classical backgroundfield in the renormalization group analysis.

The Variational Problem and Background Field in the Renormalization Group Method for Non-Linear Sigma Models