Armin Rahmani, Gia-Wei Chern
We study the Renyi mutual information of classical systems characterized by a transfer matrix. We first establish a general relationship between the Renyi mutual information of such classical mixtures of configuration states, and the Renyi entropy of a corresponding Rokhsar-Kivelson-like quantum superposition. We then focus on chiral and nonchiral kagome-ice systems, classical spin liquids on the kagome lattice. The chiral kagome ice is a critical phase realized in kagome layers of the pyrochlore spin ice in a magnetic field, while the nonchiral version has a finite correlation length and has been observed in hexagonal arrays of ferromagnetic nanoislands (artificial spin ice). Through a mapping of the chiral kagome ice to the quantum Liftshitz critical field theory, we predict a universal subleading term in the Renyi mutual information of this classical spin liquid. We verify our prediction with direct numerical transfer-matrix computations, and further demonstrate that the nonchiral kagome ice is a topologically trivial phase.
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http://arxiv.org/abs/1304.4160
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