The magnetic subsystem of nabokoite, KCu$_7$(TeO$_4$)(SO$_4$)$_5$Cl, isconstituted by copper ions forming a buckled square kagom\'e lattice decoratedby quasi-isolated ions. This combination determines peculiar physicalproperties of this compound evidenced in electron spin resonance (ESR)spectroscopy, dielectric permittivity $\varepsilon$, magnetization $M$ andspecific heat $C_p$ measurements. At lowering temperature, the magneticsusceptibility $\chi = M/H$ passes through a broad hump inherent forlow-dimensional magnetic systems at about 150 K and a sharp peak atantiferromagnetic phase transition at $T_N = 3.2 $K. The $C_p(T,H)$ curvesdemonstrate additional peak-like anomaly at $T_{peak}= 5.7$K robust to magneticfield. The latter can be ascribed to low-lying singlet excitations filling thesinglet-triplet gap in magnetic excitation spectrum of the square kagom\'elattice [J.Richter, O.Derzhko and J.Schnack, Phys. Rev. B \textbf{105} (2022)144427]. ESR spectroscopy provides indications that antiferromagnetic structurebelow $T_N$ is non-collinear. Separate issue is the observation ofantiferroelectric-type behavior in $\varepsilon$ at low temperatures, whichtentatively reduces the symmetry and partially lifts frustration of magneticinteractions of decorating copper ions with buckled square kagom\'e lattice.These complex thermodynamic and resonant properties signal the presence of twoweakly coupled magnetic subsystems in nabokoite, namely a spin-liquid in squarekagom\'e lattice layers and an antiferromagnet represented by decorating ions.
The first-order correction to the one-form sector of equations of the $3d$higher-spin theory is derived from the generating nonlinear HS system by virtueof the shifted homotopy approach. The family of solutions to the generatingsystem that disentangles equations for dynamical and topological fields in thefirst order of perturbation theory is found. This family is shown to belong tothe different cohomology class compared to the solution found earlier by thedirect methods. The related cohomology is shown to be the same as thatunderlying the mass deformation in the matter sector of $3d$ higher-spinequations.
The linear and mode-coupled contributions to higher-order anisotropic floware presented for Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 27, 39, 54.4,and 200 GeV and compared to similar measurements for Pb+Pb collisions at theLarge Hadron Collider (LHC). The coefficients and the flow harmonics'correlations, which characterize the linear and mode-coupled response to thelower-order anisotropies, indicate a beam energy dependence consistent with aninfluence from the specific shear viscosity ($\eta/s$). In contrast, thedimensionless coefficients, mode-coupled response coefficients, and normalizedsymmetric cumulants are approximately beam-energy independent, consistent witha significant role from initial-state effects. These measurements could provideunique supplemental constraints to (i) distinguish between differentinitial-state models and (ii) delineate the temperature ($T$) and baryonchemical potential ($\mu_{B}$) dependence of the specific shear viscosity$\frac{\eta}{s} (T, \mu_B)$.