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

Fundamental Models on the Lattice

L. D. Faddeev, Leon A. Takhtajan

Springer eBooksJan 1, 19873 citations

Green functions for general lattice models

William A. Schwalm, Brian Moritz, Mizuho K. Schwalm +1 more

APSMar 1, 20000 citations

Exact Solution Of The Ising Model On The 15 X 15 Square Lattice With Free Boundary Conditions

Seung‐Yeon Kim

The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of arbitrary size. For the first time, the exact solution of the Ising model on the square lattice with free boundary conditions is obtained after classifying all ) spin configurations with the microcanonical transfer matrix. Also, the phase transitions and critical phenomena of the square-lattice Ising model are discussed using the exact solution on the square lattice with free boundary conditions.The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of arbitrary size. For the first time, the exact solution of the Ising model on the square lattice with free boundary conditions is obtained after classifying all ) spin configurations with the microcanonical transfer matrix. Also, the phase transitions and critical phenomena of the square-lattice Ising model are discussed using the exact solution on the square lattice with free boundary conditions.

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer EngineeringNov 20, 20110 citations

Exact solution of the Anderson lattice model with infinite-range hopping

Canio Noce, Alfonso Romano, Carmine Lubritto

Physics Letters ASep 1, 19956 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).