Exact solutions for perpendicular susceptibilities of kagomé and decorated-kagomé Ising models

For more than two decades, exact and explicit solutions for the initial isothermal transverse susceptibility ${\chi }_{\perp }$(T) of the quantum-mechanical Ising model ferromagnet have been known on the honeycomb, square, and triangular lattices but not as yet on the kagomé lattice which is the only other regular lattice in two dimensions. Recently, however, exact solutions have been found for localized even-number correlations of the ferromagnetic kagomé Ising model, rendering its ${\chi }_{\perp }$(T) exactly calculable. Similar to the other three regular lattices, the resulting continuous curve for ${\chi }_{\perp }$(T)/${\chi }_{\perp }$(0) shows both a weak (energy-type) singularity at the critical temperature $T_c$ where ${\chi }_{\perp }$($T_c$)/${\chi }_{\perp }$(0)=1.1426. . . and a rounded maximum at $T_{\max >\mathrm{}{T}_c}$ with the parameters of this maximum given by ${\chi }_{\perp }^{\max }$/${\chi }_{\perp }$(0)=1.1945. . . at $T_{\max }$/$T_c$=1.0994. . . . The exact solution for ${\chi }_{\perp }$(T) of the decorated-kagomé Ising-model ferromagnet is also obtained having modified features illustrating the effects of the decoration spins (singly decorated bonds) upon ${\chi }_{\perp }$(T).