We report on a search for heavy neutrinos in B-meson decays. The results are obtained using a data sample that contains 772 × 10 6 B B pairs collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. No signal is observed and upper limits are set on mixing of heavy neutrinos with left-handed neutrinos of the Standard Model in the mass range 0.5 GeV/c 2 − 5.0 GeV/c 2 .

We report measurement of the cross section of e þ e − → π þ π − ψð2SÞ between 4.0 and 5.

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Abstract. Antiferromagnetic Heisenberg spin chains with various spin values (S = 1/2, 1, 3/2, 2, 5/2) are studied numerically with the quantum Monte Carlo method. Effective spin S chains are realized by ferromagnetically coupling n = 2S antiferromagnetic spin chains with S = 1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, T /J ≈ 0.01. The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap ∆, the correlation length and the uniform susceptibility in the temperature range ∆ < T < J are well predicted by the semi-classical theory of Damle and Sachdev.

Sr 2 Cu 3 O 4 Cl 2 has Cu I and Cu II subsystems, forming interpenetrating S 1͞2 square lattice Heisenberg antiferromagnets. The classical ground state is degenerate, due to frustration of the intersubsystem interactions. Magnetic neutron scattering experiments show that quantum fluctuations cause a two dimensional Ising ordering of the Cu II 's, lifting the degeneracy, and a dramatic increase of the Cu I out-of-plane spin-wave gap, unique for order out of disorder. The spin-wave energies are quantitatively predicted by calculations which include quantum fluctuations. PACS numbers: 75.30.Ds, 75.10.Jm, 75.25. + z, 75.45. + j The classical ground states of many magnetic systems are degenerate due to frustration. Quantum or thermal fluctuations often lift this degeneracy, yielding order due to disorder [1][2][3][4]. For example, when a system can be separated into two Heisenberg antiferromagnetic (AFM) sublattices, so that the molecular field of the spins in each sublattice vanishes on the spins of the other, then classically the sublattices order independently of each other, the ground state is degenerate, and the excitation spectrum contains two distinct sets of zero energy (Goldstone) modes, reflecting the fact that these subsystems can be rotated independently without cost in energy. As shown by Shender, quantum spin-wave (SW) interactions prefer collinearity of the spins in the two sublattices [2]. Concomitantly, this also generates a fluctuation driven gap in the SW spectrum. Indeed, such a gap was hypothesized in the garnet Fe 2 Ca 3 ͑GeO 4 ͒ 3 [5]. Since a similar gap could also arise from crystalline magnetic anisotropy, the final identification was rather complex.In parallel to these developments, the discovery of high temperature superconductivity triggered much work on the magnetism in lamellar copper oxides. These materials contain CuO 2 planes, whose two-dimensional (2D) spin fluctuations can be modeled well by the S 1͞2 square lattice quantum Heisenberg antiferromagnet (SLQHA) [6].The above two advances combine in the isostructural compounds Sr 2 Cu 3 O 4 Cl 2 and Ba 2 Cu 3 O 4 Cl 2 (2342). In the present paper, we show that these materials offer a dramatic and clear demonstration of ordering due to fluctuations. As shown in Fig. 1(a), the CuO 2 plane is replaced in 2342 by a Cu 3 O 4 one, which contains an additional Cu 21 II ion at the center of every second plaquette of the original Cu I O 2 square lattice [7]. The configuration in the neighboring plane is obtained by translating the whole plane by ͑ a 2ā 2 ͒. In the plane, the Cu I and Cu II subsystems form interpenetrating S 1͞2 SLQHA's with exchange interactions J I and J II . The isotropic interaction J I-II between these subsystems is frustrated; that is, its molecular field vanishes as described above, and one needs nontrivial theories to explain their ordering and SW gaps. Experimentally, 2342 exhibits AFM order of the Cu I 's and Cu II 's below the Néel temperatures T N,I and T N,II , respectively [8,9]. For temperatures T . T N,II , the...