Abstract
Two- and three-dimensional Ising-type systems are considered in the finite-cross-section cylindrical geometry. An interface is forced along the cylinder (strip in 2d) by the antiperiodic or +− boundary conditions. Detailed predictions are presented for the largest asymptotically degenerate set of the transfer matrix eigenvalues. For rough interfaces, i.e., for 0<T<T c in 2d,T R<T<T c in 3d, the eigenvalues are split algebraically, and the spectral gaps are governed by thesurface stiffness coefficient. For “rigid” interfaces, i.e., 0<T<T R in 3d, the eigenvalues are split exponentially, with the gaps determined by thestep free energy.
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Privman, V., Švrakić, N.M. Asymptotic degeneracy of the transfer matrix spectrum for systems with interfaces: Relation to surface stiffness and step free energy. J Stat Phys 54, 735–754 (1989). https://doi.org/10.1007/BF01019773
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DOI: https://doi.org/10.1007/BF01019773