As liquids crystallize into solids on cooling, spins in magnets generally form periodic order. However, three decades ago, it was theoretically proposed that spins on a triangular lattice form a liquidlike disordered state at low temperatures. Whether or not a spin liquid is stabilized by geometrical frustration has remained an active point of inquiry ever since. Our thermodynamic and neutron measurements on NiGa2S4, a rare example of a two-dimensional triangular lattice antiferromagnet, demonstrate that geometrical frustration stabilizes a low-temperature spin-disordered state with coherence beyond the two-spin correlation length. Spin liquid formation may be an origin of such behavior.

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When we form a structure of plasmas distributed in a certain space in which electromagnetic waves propagate, such a plasma structure serves as a different medium from a homogeneous bulk plasma. We can also enhance or generate novel functions of the plasmas when we add other structural materials such as functional components. That is to say, when we estimate such a medium from the material properties such as permittivity, permeability and conductivity, it shows extraordinary and/or functional effects that arise from the synthesis of the structure. We call such an artificial material a plasma metamaterial. In this review, starting from a fundamental understanding of electromagnetic wave propagation in and around plasmas, we review the new functions of plasmas as metamaterials, including a photonic-crystal-like behavior, a negative refractive index state and a nonlinear bifurcated electric response, by describing specific plasma structures. In addition, we survey some specific applications of such media and predict a feasible scientific expansion of this field in the near future.

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Tunneling conductance through two quantum dots, which are connected in series to left and right leads, is calculated by using the numerical renormalization group method. As the hopping between the dots increases from very small value, the following states continuously appear; (i) Kondo singlet state of each dot with its adjacent-site lead, (ii) singlet state between the local spins on the dots, and (iii) double occupancy in the bonding orbital of the two dots. The conductance shows peaks at the transition regions between these states. Especially, the peak at the boundary between (i) and (ii) has the unitarity limit value of 2e 2 /h because of coherent connection through the lead-dot-dotlead. For the strongly correlated cases, the characteristic energy scale of the coherent peak shows anomalous decrease relating to the quantum critical transition known for the two-impurity Kondo effect. The two dots systems give the new realization of the two-impurity Kondo problem.

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