Perpendicular susceptibility and geometrical frustration of two-dimensional kagomé Ising antiferromagnet

We present perpendicular susceptibility of antiferromagnetic kagomé Ising model obtained from the exact solutions of localized even-number correlations. The susceptibility is calculated with nearest-neighbor pair interactions where strong frustration prevents long-range ordering and with triplet (three-spin) interactions which has no frustration but the system remains disordered down to T=0 temperature. At the zero temperature limit the perpendicular susceptibility for the nearest-neighbor interaction model diverges while it is constant in the triplet interaction model. Both models with and without frustrations show finite residual entropy at the zero temperature limit. Finally, these results are compared with the susceptibilities of two-dimensional kagomé ferromagnetic [1] and triangular antiferromagnetic Ising models. Our findings suggest that the perpendicular susceptibility can be a measure of the degree of frustration of two-dimensional Ising spin systems[2].

[1] J.H. Barry and M. Khatun, Phys. Rev B 35, 8601 (1987)
[2] K.A. Muttalib, M. Khatun, and J.H. Barry, Phys. Rev B (accepted for publication, 2017)