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International Journal of Modern Physics B

KAGOME APPROXIMATION FOR 3 He ON HUSIMI LATTICE WITH TWO- AND THREE-SITE EXCHANGE INTERACTIONS

N.S. Ananikian, Vahan Hovhannisyan, H. A. Lazaryan

Published Dec 10, 2010• 19 citations
Publisher

Abstract

The Ising approximation of the Heisenberg model in a strong magnetic field, with two-, and three-spin exchange interactions are studied on a Husimi lattice. This model can be considered as an approximation of the third layer of 3 He absorbed on the surface of graphite (kagome lattice). Using dynamic approach, we have found exact recursion relation for the partition function. For different values of exchange parameters and temperature, the diagrams of magnetization are plotted and showed that magnetization properties of the model vary from ferromagnetic to antiferromagnetic depending on the value of model parameters. For antiferromagnetic case magnetization plateau at 1/3 of saturation field is obtained. Lyapunov exponent for recursion relation are considered and showed absence of bifurcation points in thermodynamic limit. The Yang–Lee zeros are analyzed in terms of neutral fixed points and showed that Yang–Lee zeros of the model are located on the arcs of the circle with the radius R = 1.

DOI
10.1142/s0217979210054324

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Physical Review B•Feb 23, 2005•22 citations
The Ising approximation of the Heisenberg model in a strong magnetic field, with two-, and three-spin exchange interactions are studied on a Husimi lattice. This model can be considered as an approximation of the third layer of 3 He absorbed on the surface of graphite (kagome lattice). Using dynamic approach, we have found exact recursion relation for the partition function. For different values of exchange parameters and temperature, the diagrams of magnetization are plotted and showed that magnetization properties of the model vary from ferromagnetic to antiferromagnetic depending on the value of model parameters. For antiferromagnetic case magnetization plateau at 1/3 of saturation field is obtained. Lyapunov exponent for recursion relation are considered and showed absence of bifurcation points in thermodynamic limit. The Yang–Lee zeros are analyzed in terms of neutral fixed points and showed that Yang–Lee zeros of the model are located on the arcs of the circle with the radius R = 1.
The Ising approximation of the Heisenberg model in a strong magnetic field, with two-, and three-spin exchange interactions are studied on a Husimi lattice. This model can be considered as an approximation of the third layer of 3He absorbed on the surface of graphite (kagome lattice). Using dynamic approach we have found exact recursion relation for the partition function. For different values of exchange parameters and temperature the diagrams of magnetization are plotted and showed that magnetization properties of the model vary from ferromagnetic to antiferromagnetic depending from the value of model parameters. For antiferromagnetic case magnetization plateau at 1/3 of saturation field is obtained. Lyapunov exponent for recursion relation are considered and showed absents of bifurcation points in thermodynamic limit. The Yang-Lee zeros are analyzed in terms of neutral fixed points and showed that Yang-Lee zeros of the model are located on the arcs of the circle with the radius R=1.
Fisher zeros for the partition function with respect to a temperature-dependent parameter are studied. The Ising approximation for Heisenberg model with two- and three-site exchange interactions on the Husimi lattice was used. This model approximates the third layer of 3 He, absorbed on the surface of graphite (kagome lattice). Using dynamic approach, we have found an exact recursion relation for the partition function. The presence of a phase transition, both in the real and complex regions on the temperature plane was shown.
The spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is exactly solved in a magnetic field within the framework of the generalized star-triangle transformation and the method of exact recursion relations. The generalized star-triangle transformation establishes an exact mapping correspondence with the effective spin-1/2 Ising model on a triangular Husimi lattice with a temperature-dependent field, pair and triplet interactions, which is subsequently rigorously treated by making use of exact recursion relations. The ground-state phase diagram of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice, which bears a close resemblance with a triangulated kagomé lattice, involves, in total, two classical and three quantum ground states manifested in respective low-temperature magnetization curves as intermediate plateaus at 1/9, 1/3, and 5/9 of the saturation magnetization. It is verified that the fractional magnetization plateaus of quantum nature have character of either dimerized or trimerized ground states. A low-temperature magnetization curve of the spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice may exhibit either no intermediate plateau, a single 1/3 plateau, a single 5/9 plateau, or a sequence of 1/9, 1/3, and 5/9 plateaus depending on a character and relative size of two considered coupling constants.
We consider the Heisenberg model with two-, and three-spin exchange interactions on a zigzag ladder in a strong magnetic field. Using the recursion method for the partition function in Ising approximation we have found exact results for the magnetization. We have shown the existence of magnetization plateaus in the case of mutual two-, and three-spin exchanges at low temperatures and different exchange parameters. The system exhibits different magnetic behaviors, depending on the values of the exchange parameters.
The magnetic and entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on a triangulated Kagome lattice are analyzed by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. Because of the separable character of Ising-type exchange interactions between the Heisenberg trimers the calculation of quantum entanglement in a self-consistent field can be performed for each of the trimers individually. The concurrence in terms of three qubit isotropic Heisenberg model in effective Ising field is non-zero even in the absence of a magnetic field. The magnetic and entanglement properties exhibit common (plateau and peak) features observable via (antferromagnetic) coupling constant and external magnetic field. The critical temperature for the phase transition and threshold temperature for concurrence coincide in the case of antiferromagnetic coupling between qubits. The existence of entangled and disentangled phases in saturated and frustrated phases is established.
A two-dimensional Ising model on a particular topological structure, a ``triangles-in-triangles'' Kagom\'e structure, which is called a triangular-Kagom\'e lattice, is investigated. In this model, we consider two interaction parameters Jaa{J}_{aa}Jaa​ and Jab{J}_{ab}Jab​, 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 Jaa{J}_{aa}Jaa​. 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.