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

Physical review. B, Condensed matterJun 1, 198716 citations

Exactly Solvable Decorated-Kekulé-lattice Kitaev Model

Tomonari Mizoguchi

We propose the decorated-Kekulé-lattice Kitaev model, which is exactly solvable at any temperature. Similar to the decorated honeycomb model proposed in our previous work [J. Phys. Soc. Jpn. 91, 124709 (2022)], the exact solvability arises from the fact that the spins on the decorated sites become conserved quantities (i.e., classical variables) and serve as an effective field acting on the remaining spins. For a given sector of the classical variables, the remaining spins are described by the Hamiltonian of ensemble of decoupled two-site transverse Ising models, with eigenenergies being independent of the configuration of the classical variables. This enables us to calculate the partition function exactly, and hence the thermodynamic quantities are obtained at any temperature. Our result indicates that the site decoration for the compass-type models is a ubiquitous method to obtain the models that are exactly solvable at finite temperature.We propose the decorated-Kekulé-lattice Kitaev model, which is exactly solvable at any temperature. Similar to the decorated honeycomb model proposed in our previous work [J. Phys. Soc. Jpn. 91, 124709 (2022)], the exact solvability arises from the fact that the spins on the decorated sites become conserved quantities (i.e., classical variables) and serve as an effective field acting on the remaining spins. For a given sector of the classical variables, the remaining spins are described by the Hamiltonian of ensemble of decoupled two-site transverse Ising models, with eigenenergies being independent of the configuration of the classical variables. This enables us to calculate the partition function exactly, and hence the thermodynamic quantities are obtained at any temperature. Our result indicates that the site decoration for the compass-type models is a ubiquitous method to obtain the models that are exactly solvable at finite temperature.

Journal of the Physical Society of JapanJan 23, 20260 citations

Anomalous behavior in semi-decorated square Ising lattice

H.-T. Yeh

PhysicaMar 1, 19732 citations

{T}_{c}

where ${\ensuremath{\chi}}_{\ensuremath{\perp}}$(

{T}_{c}

)/${\ensuremath{\chi}}_{\ensuremath{\perp}}$(0)=1.1426. . . and a rounded maximum at

{T}_{\mathrm{max}>{T}_{c}}

with the parameters of this maximum given by ${\ensuremath{\chi}}_{\ensuremath{\perp}}^{\mathrm{max}}$/${\ensuremath{\chi}}_{\ensuremath{\perp}}$(0)=1.1945. . . at

{T}_{\mathrm{max}}

{T}_{c}

=1.0994. . . . The exact solution for ${\ensuremath{\chi}}_{\ensuremath{\perp}}$(T) of the decorated-kagom\'e Ising-model ferromagnet is also obtained having modified features illustrating the effects of the decoration spins (singly decorated bonds) upon ${\ensuremath{\chi}}_{\ensuremath{\perp}}$(T).