Journal of Physics A Mathematical and General

An exact result for the Kagome lattice Ising model with magnetic field

Héctor Giacomini

Published Jan 7, 1988• 25 citations

Abstract

An anisotropic Ising model with three interaction parameters K 1 , K 2 , K 3 and a magnetic field H, formulated on the Kagome lattice, is solved exactly for an appropriate relation between K i and H. When this relation is satisfied the system becomes equivalent to a free-fermion model.

DOI: 10.1088/0305-4470/21/1/006

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Journal of Physics A Mathematical and General

An exact result for the Kagome lattice Ising model with magnetic field

Héctor Giacomini

Published Jan 7, 1988• 25 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/21/1/006

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Wentao Lu, Fa Yueh Wu

arXiv:cond-mat/0409083Physical Review EApr 18, 200515 citations

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J. Strev ka, Lucia Čanová

Acta Physica Polonica AJan 1, 20082 citations

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Jozef Strečka, Lucia Čanová

The spin-1/2 Ising model on the bow-tie lattice is exactly solved by establishing a precise mapping relationship with its corresponding free-fermion eight-vertex model. Ground-state and finite-temperature phase diagrams are obtained for the anisotropic bow-tie lattice with three different exchange interactions along three different spatial directions.

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{J}_{aa}

and

{J}_{ab}

, corresponding to the interactions among spins on the inner sites and between spins on the inner and vertex sites of the triangular in the Kagom\'e lattice, respectively. By summing over all spins at inner sites in the partition function, we arrive at the partition function of the Kagom\'e lattice. The effective interaction of the corresponding Kagom\'e lattice is always ferromagnetic, even for antiferromagnetic

{J}_{aa}

. The critical properties of the system depend only on ${J}_{aa}∕\ensuremath{\mid}{J}_{ab}\ensuremath{\mid}$. When ${J}_{aa}∕\ensuremath{\mid}{J}_{ab}\ensuremath{\mid}>\ensuremath{-}1$, the system has long range order at low temperature. However, when ${J}_{aa}∕\ensuremath{\mid}{J}_{ab}\ensuremath{\mid}<\ensuremath{-}1$, the partition function of the triangular-Kagom\'e lattice can be related to that of the Kagom\'e lattice with effective interaction at a temperature higher than its critical temperature. Therefore, the system will be in paramagnetic phase at all temperatures for ${J}_{aa}∕\ensuremath{\mid}{J}_{ab}\ensuremath{\mid}<\ensuremath{-}1$. The phase diagram for ${J}_{aa}∕\ensuremath{\mid}{J}_{ab}\ensuremath{\mid}$ is given exactly.