Abstract
We investigate the corner spin magnetization of two-dimensional ferromagnetic Ising models in various wedge geometries. Results are obtained for triangular and square lattices by numerical studies on finite wedges using the star-triangle transformation, as well as analytic calculations using corner transfer matrices and a fermionic representation of the row-to-row transfer matrix. The corner magnetizations vanish at the bulk critical temperature Tc with an exponentβ c differing from the bulk exponent. For isotropic systems with free edges we find thatβ c is given simply byβ c =π/2θ, whereθ is the angle at the corner. For apex magnetizations of conical lattices we obtain the strikingly similar resultα a=π/4θ. These formulas apply equally well to anisotropic lattices if the angleθ is interpreted as an effective angle,θ eff, determined by the relative strengths of the interactions.
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Barber, M.N., Peschel, I. & Pearce, P.A. Magnetization at corners in two-dimensional Ising models. J Stat Phys 37, 497–527 (1984). https://doi.org/10.1007/BF01010493
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DOI: https://doi.org/10.1007/BF01010493