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We compute the exact partition function of the 2D Ising Model at criticaltemperature but with nonzero magnetic field at the boundary. The modeldescribes a renormalization group flow between the free and fixed conformalboundary conditions in the space of boundary interactions. For this flow theuniversal ground state degeneracy $g$ and the full boundary state is computedexactly.Comment: Two lines in the Introduction and three references adde

EXACT PARTITION FUNCTION AND BOUNDARY STATE OF CRITICAL ISING MODEL WITH BOUNDARY MAGNETIC FIELD