We clarify elementary excitations in the ∆-chain. They are found to be 'kink'-'antikink' type domain wall excitations to the dimer singlet ground state. The characters of a kink and an antikink are quite different in this system: a kink has no excitation energy and is localized, while an antikink has a finite excitation energy and propagates. The excitation energy of a kink-antikink pair consists of a finite energy gap and a kinetic energy due to the free motion of the antikink. Variational wave functions for an antikink are studied to clarify its propagating states. All the numerical results are explained consistently based on this picture. At finite temperatures, thermally excited antikinks are moving in regions bounded by localized kinks. The origin of the low-temperature peak in the specific heat reported previously is explained and the peak position in the thermodynamic limit is estimated. 65.40.Hq, 75.50.Ee, 75.60.Ch

The three-dimensional ±J Heisenberg spin-glass model is investigated by the non-equilibrium relaxation method from the paramagnetic state. Finite-size effects in the non-equilibrium relaxation are analyzed, and the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility in the infinite-size system are obtained. The finite-time scaling analysis gives the spin-glass transition at Tsg/J = 0.21 +0.01 −0.02 and the chiral-glass transition at Tcg/J = 0.22 +0.01 −0.03 . The results suggest that both transitions occur simultaneously. The critical exponent of the spin-glass susceptibility is estimated as γsg = 1.7 ± 0.3, which makes an agreement with the experiments of the insulating and the canonical spin-glass materials. 75.10.Nr, 75.40.Mg, 64.60.Cn, 64.60.Fr

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We have performed Monte Carlo simulations on the quantum Heisenberg antiferromagnet on the kagome lattice with up to 72 spins. We have used the transfer-matrix Monte Carlo method, which enabled us to do eKcient samplings at rather low temperatures where other methods suffer from serious sign problem. Specific-heat data exhibit the double peak. Results of the chirality and shortrange spin correlations show no tendency of any magnetic ordering even at the lowest temperature we observed.Recent interest in the kagome antiferromagnet originates in the experiment of a He layer adsorbed on graphite in the mK temperature region.A peak of the specific heat was observed at the coverage p 0.18 atoms/A. , where the second layer is just filled. An unexpected finding is a lack of entropy. Namely, if we assume C oc T in the low temperature region where the experiment could not be achieved, the entropy calculated by the integration C/T is just half the expected value. 2 Therefore they speculated that some structure, or the second peak, might be present in the lower temperature region not yet observed experimentally.Elser proposed that the atoms on the second layer form the~7 x~7 triangular lattice and that a quarter of the atoms become free from the exchange interactions so that the remainder form a kagome lattice. The~7x~7 structure with respect to the first layer atoms is supported by path integral simulations. In this proposal, half the missing entropy is to come from these free spins. The other half is to be supplied by the additional low temperature peak of the specific heat. He showed the double peak by the numerical diagonalization of a small cluster and by the decoupled-cell Monte Carlo simulation. It should be noted that there is another explanation of the specific heat; the multispin interactions may play an important role in this triangular system as well as the two-body interactions.Apart from the experiment, the kagome system provides attracting problems concerning both the thermodynamic properties and the ground state, and thus numerous eKorts have been done both analytically and numerically.Classically, the kagome antiferromagnet possesses macroscopic local degeneracy in the ground states. In the quantum system, two typical structures have been considered as candidates for the ground state selected among the classical degenerate ground states by quantum fluctuations. One is a~3 x~3 structure and the other is a q = 0 structure. Within the linear spinwave theory, both states have an identical dispersionless zero-energy mode throughout the Brillouin zone. ' It is reported that higher order corrections to the spin-wave calculation lift the degeneracy and the two states are stabilized for the systems with large 8 value. A large-N expansion gives a similar result but a disordered ground state at small S. The disordered ground state is predicted by the series expansion from the Ising limit and the numerical diagonalization of finite systems. ' ' Results of the high temperature expansion depend on the orders of expansion....