We present the complete solution to a $95%$ scalar field cosmological model in which the dark matter is modeled by a scalar field $\ensuremath{\Phi}$ with the scalar potential $V(\ensuremath{\Phi}{)=V}_{0}[\mathrm{cosh}(\ensuremath{\lambda}\sqrt{{\ensuremath{\kappa}}_{0}}\ensuremath{\Phi})\ensuremath{-}1]$ and the dark energy is modeled by a scalar field \ensuremath{\Psi}, endowed with the scalar potential $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}(\ensuremath{\Psi})={V}_{0}[\mathrm{sinh}(\ensuremath{\alpha}\sqrt{{\ensuremath{\kappa}}_{0}}\ensuremath{\Psi}){]}^{\ensuremath{\beta}}.$ This model has only two free parameters, \ensuremath{\lambda} and the equation of state ${\ensuremath{\omega}}_{\ensuremath{\Psi}}.$ With these potentials, the fine-tuning and cosmic coincidence problems are ameliorated for both dark matter and dark energy and the model agrees with astronomical observations. For the scalar dark matter, we clarify the meaning of a scalar Jeans length and then the model predicts a suppression of the mass power spectrum for small scales having a wave number $kg{k}_{\mathrm{min},\ensuremath{\Phi}},$ where ${k}_{\mathrm{min},\ensuremath{\Phi}}\ensuremath{\simeq}4.5h$ ${\mathrm{Mpc}}^{\ensuremath{-}1}$ for $\ensuremath{\lambda}\ensuremath{\simeq}20.28.$ This last fact could help to explain the death of dwarf galaxies and the smoothness of galaxy core halos. From this, all parameters of the scalar dark matter potential are completely determined. The dark matter consists of an ultralight particle, whose mass is ${m}_{\ensuremath{\Phi}}\ensuremath{\simeq}1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ eV and all the success of the standard cold dark matter model is recovered. This implies that a scalar field could also be a good candidate the dark matter of the Universe.

/pdf/further-analysis-of-a-cosmological-model-with-quintessence-20svnafm28.pdf

Further analysis of a cosmological model with quintessence and scalar dark matter

Thallium copper chloride is a quantum spin liquid of $S=1/2$ ${\mathrm{Cu}}^{2+}$ dimers. Interdimer superexchange interactions give a three-dimensional magnon dispersion and a spin gap significantly smaller than the dimer coupling. This gap is closed by an applied hydrostatic pressure of approximately 2 kbar or by a magnetic field of 5.6 T, offering a unique opportunity to explore both types of quantum phase transition and their associated critical phenomena. We use a bond-operator formulation to obtain a continuous description of all disordered and ordered phases, and thus of the transitions separating these. Both pressure- and field-induced transitions may be considered as the Bose--Einstein condensation of triplet magnon excitations, and the respective phases of staggered magnetic order as linear combinations of dimer-singlet and dimer-triplet modes. We focus on the evolution with applied pressure and field of the magnetic excitations in each phase, and in particular on the gapless (Goldstone) modes in the ordered regimes which correspond to phase fluctuations of the ordered moment. The bond-operator description yields a good account of the magnetization curves and of magnon dispersion relations observed by inelastic neutron scattering under applied fields, and a variety of experimental predictions for pressure-dependent measurements.

https://arxiv.org/pdf/cond-mat/0309440.pdf

Field- and pressure-induced magnetic quantum phase transitions in TlCuCl 3

Continuing on from previous works, we present a cosmological model in which dark matter and dark energy are modelled by scalar fields Φ and Ψ, respectively, endowed with the scalar potentials V(Φ) = Vo[cosh (λ√κoΦ) - 1] and (Ψ) = o[sinh (α√κoΨ)]β. This model contains a 95% scalar field. We obtain that the scalar dark matter mass is mΦ~10-26 eV. The solution obtained allows us to recover the success of standard cold dark matter. The implications on the formation of structure are reviewed. We obtain that the minimal cut-off radio for this model is rc ~ 1.2 kpc.

https://iopscience.iop.org/article/10.1088/0264-9381/17/13/101/pdf

Quintessence and scalar dark matter in the universe

We study the behavior of Heisenberg, antiferromagnetic, integer-spin chains in the presence of a magnetic field exceeding the attendant spin gap. For temperatures much smaller than the gap, the spin chains exhibit Luttinger liquid behavior. We compute exactly both the corresponding Luttinger parameter and the Fermi velocity as a function of magnetic field. This enables the computation of a number of correlators from which we derive the spin conductance, the expected form of the dynamic structure factor relevant to inelastic neutron-scattering experiments, and NMR relaxation rates. We also comment upon the robustness of the magnetically induced gapless phase both to finite temperature and finite couplings between neighboring chains.

https://arxiv.org/pdf/cond-mat/0106037.pdf

Haldane-gapped spin chains as Luttinger liquids: Correlation functions at finite field

We have studied the ground-state phase diagram of a two-leg spin ladder with anisotropic ferromagnetic leg couplings under the influence of a symmetry-breaking transverse magnetic field by the exact diagonalization technique. In the case of antiferromagnetic coupling between legs we identified two phase transitions in the plane of magnetic field versus interchain coupling strength. The first corresponds to the transition from the gapped rung-singlet phase to the gapped stripe-ferromagnetic phase. The second represents the transition from the gapped stripe-ferromagnetic phase into the fully polarized ferromagnetic phase.

Spin ladder with anisotropic ferromagnetic legs in a transverse magnetic field

We present a theoretical analysis of the properties of low-dimensional quantum antiferromagnets in applied magnetic fields. In a nonlinear a model description, we use a spin stiffness analysis, a 1/N expansion, and a renormalization group approach to describe the broken-symmetry regimes of finite magnetization, and, in cases of most interest, a low-field regime where symmetry is restored by quantum fluctuations. We compute the magnetization, critical fields, spin correlation functions, and decay exponents accessible by nuclear magnetic resonance experiments. The model is relevant to many systems exhibiting Haldane physics, and provides good agreement with data for the two-chain spin ladder compound CuHpCl.

B. Normand

Papers

Nonlinear σ model treatment of quantum antiferromagnets in a magnetic field