Exact solution of the geometrically frustrated spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice

Details Exact solution of the geometrically frustrated spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice Exact solution of the geometrically frustrated spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice

2008-02-12

arxiv.org/abs/0802.1582v3

Phys. Rev. B 78 (2008) 024427

Physics

Condensed Matter

Statistical Mechanics

13 pages, 7 figures, submitted to Phys. Rev. B

Scientific paper

10.1103/PhysRevB.78.024427

The geometric frustration of the spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice is investigated within the framework of an exact analytical method based on the generalized star-triangle mapping transformation. Ground-state and finite-temperature phase diagrams are obtained along with other exact results for the partition function, Helmholtz free energy, internal energy, entropy, and specific heat, by establishing a precise mapping relationship to the corresponding spin-1/2 Ising model on the Kagome lattice. It is shown that the residual entropy of the disordered spin liquid phase is for the quantum Ising-Heisenberg model significantly lower than for its semi-classical Ising limit (S_0/N_T k_B = 0.2806 and 0.4752, respectively), which implies that quantum fluctuations partially lift a macroscopic degeneracy of the ground-state manifold in the frustrated regime. The investigated model system has an obvious relevance to a series of polymeric coordination compounds Cu_9X_2(cpa)_6 (X=F, Cl, Br and cpa=carboxypentonic acid) for which we made a theoretical prediction about the temperature dependence of zero-field specific heat.

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