Transfer matrices as the free-energy of topological excitations

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Transfer matrices allow us to deduce the thermodynamics of translationally invariant systems, which for large systems relates the free energy to the maximal eigenvalue. However, what do the excitations correspond to physically? The focus of my research is showing that, exactly in the case of the Ising model, these excitations correspond to topological objects in the underlying lattice. The idea is to generalise this to other, more complicated, models in statistical mechanics.