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Physical review. B, Condensed matter

Thermodynamical properties of an antiferromagnetic Heisenberg spin system on a fractal lattice of dimension between one and two

Piotr Tomczak

Published Jan 1, 1996• 10 citations
Publisher

Abstract

The Suzuki-Takano quantum decimation technique is applied to the antiferromagnetic, nearest-neighbor, frustrated Heisenberg spin-\textonehalf{} system attached to a lattice with dimension $d=\frac{\mathrm{ln}3}{\mathrm{ln}2}$. Some thermodynamical functions are calculated. The temperature dependence of the specific heat is very similar to that obtained for the Heisenberg spin system on a kagom\'e lattice.

DOI
10.1103/physrevb.53.r500

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The Suzuki-Takano quantum decimation technique is applied to the antiferromagnetic, nearest-neighbor, frustrated Heisenberg spin-\textonehalf{} system attached to a lattice with dimension d=ln3ln2d=\frac{\mathrm{ln}3}{\mathrm{ln}2}d=ln2ln3​. Some thermodynamical functions are calculated. The temperature dependence of the specific heat is very similar to that obtained for the Heisenberg spin system on a kagom'e lattice.
We consider the S = 1 / 2 antiferromagnetic Heisenberg model on a frustrated kagome-lattice bilayer with strong nearest-neighbor interlayer coupling and examine its low-temperature magnetothermodynamics using a mapping onto a rhombi gas on the kagome lattice. Besides, we use finite-size numerics to illustrate the validity of the classical lattice-gas description. Among our findings there are (i) the absence of an order-disorder phase transition and (ii) the sensitivity of the specific heat at low temperatures to the shape of the system just below the saturation magnetic field even in the thermodynamic limit.
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Thermodynamic properties are studied for the one-dimensional spin-1/2 Heisenberg antiferromagnet with antiferromagnetic first- and second-neighbor exchange interactions. The internal energy, the specific heat, and the two-spin correlation function are calculated by means of the cluster transfer matrix method based on the Suzuki-Trotter equivalence theorem. Special attention is paid to the asymptotic behavior of the two-spin correlation function in the long-distarace limit. It is found that for a certain range of values of the interaction constants and of the temperature, the two-spin correlation function decays with an incommensurate or a higher-order commensurate oscillation as a function of the distance between two spins. We also find that there exists a quantum analog of the disorder line, on which the two-spin correlation function changes its character.
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We analyze the thermodynamic properties of the spin-SSS two-dimensional quantum Heisenberg antiferromagnet on a square lattice with nearest and next-nearest neighbor couplings in the N\'eel phase (J2∕J1<0.4)({J}_{2}∕{J}_{1}<0.4)(J2​∕J1​<0.4) employing the quantum hierarchical reference theory, a nonperturbative implementation of the renormalization group method to quantum systems. We investigate the staggered susceptibility, the structure factors, and the correlation length at finite temperature and for different values of the frustration ratio. From the finite temperature results, we also extrapolate ground state properties, such as spin stiffness and spontaneous staggered magnetization, providing an estimate of the extent of quantum corrections. The behavior of these quantities as a function of frustration may provide some hints on the breakdown of the N\'eel phase at zero temperature for larger values of J2{J}_{2}J2​.