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A classical Heisenberg Hamiltonian, to which is added single-ion anisotropy and antisymmetric Dzialoshinsky-Moriya interactions is studied with use of Wilson theory. The phase diagram is obtained; it consists of ferromagnetic, spiral, and ferromagnetic-spiral regions, with critical exponents that are Ising-like, xy-like, and Heisenberg-like, respectively. These results lead to the conclusion that breaking of exchange symmetry does not change the nature of the phase transition. Crossover behavior is also discussed.Consider a system composed of three-dimensional classical spins situated on a ^-dimensional "hypercubical" lattice and described by the model Hamiltonian 3C=3C 1 + X 2 + 3C 3 . Herewhere spins Si = (S ixJ S iy , S ie ) and Sj interact only if lattice sites i, j are nearest neighbors, and the energy of a pair of parallel spins is -J. The second term in the Hamiltonian is the singleion anisotropy term, presumably due to interactions such as crystal fields:The third term is a Dzialoshinski-Moriya interaction, 1where the prime on the summation means that it is restricted to nearest-neighbor pairs of spins that are on adjacent "hyperplanes" (this means Yj-r { = z, where z is a nearest-neighbor vector in the z lattice direction). Although the most general Dzialoshinski-Moriya interaction is A •S { x Sj, we have set 'A=A 3 z in (lc) without loss of generality. The impetus for this study is as follows:(1) There are many magnetic materials 2 that display complex helical spin configurations in their ordered states, although there exists little analysis beyond mean-field theory. The Hamiltonian 3C is capable of describing systems with helical ordering [cf. Fig. 1].(2) The antisymmetric Dzialoshinski-Moriya interaction is of interest in its own right. From spin-orbit coupling theory, it is known to be the cause of "weak" ferromagnetism in certain materials (e.g., hematite, 3 a-Fe 2 0 3 ). Moreover, in a recent Letter, Melcher 4 has shown that the spin-wave dispersion relation includes a linear term, oo(q) =aq + bq 2 , where a and b are functions of J, D, and A 3 , and a = 0 unless A 3 ^0, leading one to suspect possible effects of nonzero A 3 on thermodynamic properties in general and on critical properties in particular.(3) The interaction 3C 3 provides an opportunity to test the effect of breaking exchange symmetry on critical properties, 5 " 6 since the antisymmetric interaction A^SjXSj changes sign upon interchange of S { and S i? whereas previously studied models of critical behavior are symmetric under this interchange.In this work I study the critical behavior of K using the Wilson renormalization group ap-\ V fW/ FIG. 1. Pictoral representation of the phase diagram of the Hamiltonian 3^ = 3^ + ^ +3C 3 . (a), (b), (e) The ordered states for the cases (i) D>A 3 2 , (ii) D

The three&pin interaction Hamiltonian X = --J3Z«»& saba&a» -HZt s; -H'Z& 0& (the s and 0 spins belong to different sublattices) is solved for some two4imensional lattices by a generalized star-triangle transformation. The H' = 0 internal energy, specific heat, and magnetization are explicitly calculated, and the singularity structures of other functions (e.g.,x) are studied. Although the actual critical-point exponents remain the same as for systems with two&pin interaction, the three&pin interaction gives rise to different amplitude and background terms. In particular, the H' = 0 magnetization is nonzero for all finite T, because of the lack of spin-reversal symmetry; the diameter is seen explicitly to have an energy singularity, with critical exponent 1af.

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The choroid plexus (CP) in brain ventricles secrete cerebrospinal fluid (CSF) that bathes the adjacent subventricular zone (SVZ); the latter is the largest neurogenic region in adult brain harboring neural stem/progenitor cells (NSPCs) and supplies newborn neurons to the olfactory bulb (OB) for normal olfaction. We discovered the presence of a CP-SVZ regulatory (CSR) axis in which the CP, by secreting small extracellular vesicles (sEVs), regulated adult neurogenesis in the SVZ and maintained olfaction. The proposed CSR axis was supported by 1) differential neurogenesis outcomes in the OB when animals treated with intracerebroventricular (ICV) infusion of sEVs collected from the CP of normal or manganese (Mn)-poisoned mice, 2) progressively diminished SVZ adult neurogenesis in mice following CP-targeted knockdown of SMPD3 to suppress CP sEV secretion, and 3) compromised olfactory performance in these CP-SMPD3-knockdown mice. Collectively, our findings demonstrate the biological and physiological presence of this sEV-dependent CSR axis in adult brains.