Pirogov-Sinai theory with new contours for symmetric models

• Main Authors: Ganikhodjaev, Nasir, Rozikov, Utkir Abdulloevich
• Format: Article
• Language: English
• Published: World Scientific Publishing Co. 2008
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/1644/1/Pirogov_Sinai%2C2008%2C537.zip; http://irep.iium.edu.my/1644/; http://www.worldscinet.com/ijgmmp/05/0504/S0219887808002928.html
• Institution: Universiti Islam Antarabangsa Malaysia

The contour argument was introduced by Peierls for two dimensional Ising model. Peierls benefited from the particular symmetries of the Ising model. For non-symmetric models the argument was developed by Pirogov and Sinai. It is very general and rather difficult. Intuitively clear that the Peierls argument does work for any symmetric model. But contours defined in Pirogov–Sinai theory do not work if one wants to use Peierls argument for more general symmetric models. We give a new definition of contour which allows relatively easier proof to the main result of the Pirogov–Sinai theory for symmetric models. Namely, our contours allow us to apply the classical Peierls argument (with contour removal operation).