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We compute rigorously the ground and equilibrium states for Kitaev's model in2D, both the finite and infinite version, using an analogy with the 1D Isingferromagnet. Next, we investigate the structure of the reduced dynamics in thepresence of thermal baths in the Markovian regime. Special attention is paid tothe dynamics of the topological freedoms which have been proposed for storingquantum information

A statistical mechanics view on Kitaev's proposal for quantum memories