Perpendicular susceptibility and geometrical frustration in two-dimensional Ising antiferromagnets: Exact solutions

Abstract

Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility ${\ensuremath{\chi}}_{\ensuremath{\perp}}$ for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled ${\ensuremath{\chi}}_{\ensuremath{\perp}}$ can be used as a quantitative measure of the degree of frustration in Ising spin systems.