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The contour argument was introduced by Peierls for two dimensional Isingmodel. Peierls benefited from the particular symmetries of the Ising model. Fornon-symmetric models the argument was developed by Pirogov and Sinai. It isvery general and rather difficult. Intuitively clear that the Peierls argumentdoes work for any symmetric model. But contours defined in Pirogov-Sinai theorydo not work if one wants to use Peierls argument for more general symmetricmodels. We give a new definition of contour which allows relatively easierprove the main result of the Pirogov-Sinai theory for symmetric models. Namely,our contours allow us to apply the classical Peierls argument (with contourremoval operation).

PIROGOV–SINAI THEORY WITH NEW CONTOURS FOR SYMMETRIC MODELS