We build a holographic $s$-wave conductor/superconductor model and an insulator/superconductor model in the four-dimensional conformal anomaly corrected~(CAC) AdS gravity. The effects of CAC parameter $alpha$ are studied using both numerical and anal
ytical methods in the probe approximation. Concretely, when the CAC parameter increases, the critical temperature increases for the conductor/superconductor phase transition, while the critical chemical potential decreases for the insulator/superconductor case, which suggests that the increasing CAC parameter enhances both superconducting phase transitions. Meanwhile, below the critical temperature or beyond the critical chemical potential, the scalar hair begins to condense, and the condensed phases are found to be thermodynamically stable. The critical behaviors obtained from numerics are confirmed by our analytical analysis. For the parameters we are considering, the energy gap in the conductor/superconductor model decreases monotonically by increasing the CAC parameter, while for the insulator/superconductor model the energy of quasiparticle excitations decreases with the CAC parameter.
It has been found that the geometrical diagnostic methods can break the degeneracy for dark energy models. In this paper, we investigate the $Om$ diagnostic, the statefinder hierarchy $S_{n}$ and the composite null diagnostic ${S_{n},epsilon}$ for th
e Tsallis holographic dark energy models with interactions. We find that model parameters and the forms of interaction will influence the values of diagnostic parameters or the trends of the evolutionary trajectories for each model. Moreover, the statefinder hierarchy $S_{3}^{(1)}$ together with ${S_{3}^{(1)},epsilon}$ could give good diagnostic results. Furthermore, we also obtain some issues of cosmological structure by means of the composite null diagnostic.
Based on the dynamics of single scalar field slow-roll inflation and the theory of reheating, we investigate the generalized natural inflationary (GNI) model. Concretely, we give constraints on the scalar spectral index $n_{s}$ and tensor-to scalar r
atio $r$ for $Lambda$CDM $+r$ model according to the latest data from Plack 2018 TT,TE,EE+lowE+lensing (P18) and BICEP2/Keck 2015 season (BK15), i.e., $n_{s}=0.9659pm0.0044$ at $68%$ confidence level (CL) and $r<0.0623$ at $95%$CL. We find that the GNI model is favored by P18 plus BK15 in the ranges of $log_{10}(f/M_{p})=0.62^{+0.17}_{-0.18}$ and $m=0.35^{+0.13}_{-0.23}$ at $68%$CL. In addition, the corresponding predictions of the general and two-phase reheating are respectively discussed. It follows that the parameter $m$ has the significant effect on the model behaviors.
We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity (GR) obtained by adding a term $m^{2n-2}RBox^{-n}R$ to the Einstein-Hilbert action. Moreover, in order to get some insight
on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter $varepsilon$ for different $n$. By analysis we give the constraints on the model parameters $varepsilon$.
In the probe limit, we investigate the nonlinear electrodynamical effects of the both exponential form and the logarithmic form on the holographic paramagnetism-ferromagnetism phase transition in the background of a Schwarzschild-AdS black hole space
time. Moreover, by comparing the exponential form of nonlinear electrodynamics with the logarithmic form of nonlinear electrodynamics and the Born-Infeld nonlinear electrodynamics which has been presented in Ref.~cite{Wu:2016uyj}, we find that the higher nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder form in the case without external field. Furthermore, the increase of nonlinear parameter b will result in extending the period of the external magnetic field. Especially, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noticeable.
In the probe limit, we investigate holographic paramagnetism-ferromagnetism phase transition in the four-dimensional (4D) and five-dimensional(5D) Lifshitz black holes by means of numerical and semi-analytical methods, which is realized by introducin
g a massive 2-form field coupled to the Maxwell field. We find that the Lifshitz dynamical exponent $z$ contributes evidently to magnetic moment and hysteresis loop of single magnetic domain quantitatively not qualitatively. Concretely, in the case without external magnetic field, the spontaneous magnetization and ferromagnetic phase transition happen when the temperature gets low enough, and the critical exponent for the magnetic moment is always $1/2$, which is in agreement with the result from mean field theory. And the increasing $z$ enhances the phase transition and increases the DC resistivity which behaves as the colossal magnetic resistance effect in some materials. Furthermore, in the presence of the external magnetic field, the magnetic susceptibility satisfies the Cure-Weiss law with a general $z$. But the increase of $z$ will result in shortening the period of the external magnetic field.
We construct a class of generalized non-local gravity (GNLG) model which is the modified theory of general relativity (GR) obtained by adding a term $m^{2n-2} RBox^{-n}R$ to the Einstein-Hilbert action. Concretely, we not only study the gravitational
equation for the GNLG model by introducing auxiliary scalar fields, but also analyse the classical stability and examine the cosmological consequences of the model for different exponent $n$. We find that the half of the scalar fields are always ghost-like and the exponent $n$ must be taken even number for a stable GNLG model. Meanwhile, the model spontaneously generates three dominant phases of the evolution of the universe, and the equation of state parameters turn out to be phantom-like. Furthermore, we clarify in another way that exponent $n$ should be even numbers by discuss the spherically symmetric static solutions in Newtonian gauge. It is worth stressing that the results given by us can include ones in refs. [28, 34] as the special case of $n=2$.
In this paper, we investigate in some detail the holographic ferromagnetic phase transition in an AdS${_4}$ black brane background by introducing a massive 2-form field coupled to the Maxwell field strength in the bulk. In the two probe limits, one i
s to neglect the back reaction of the 2-form field to the background geometry and to the Maxwell field, and the other to neglect the back reaction of both the Maxwell field and the 2-form field, we find that the spontaneous magnetization and the ferromagnetic phase transition always happen when the temperature gets low enough with similar critical behavior. We calculate the DC resistivity in a semi-analytical method in the second probe limit and find it behaves as the colossal magnetic resistance effect in some materials. In the case with the first probe limit, we obtain the off-shell free energy of the holographic model near the critical temperature and compare with the Ising-like model. We also study the back reaction effect and find that the phase transition is always second order. In addition, we find an analytical Reissner-Norstrom-like black brane solution in the Einstein-Maxwell-2-form field theory with a negative cosmological constant.
In the probe limit, we numerically build a holographic $p$-wave superfluid model in the four-dimensional Lifshitz black hole coupled to a Maxwell-complex vector field. We observe the rich phase structure and find that the Lifshitz dynamical exponent
$z$ contributes evidently to the effective mass of the matter field and dimension of the gravitational background. Concretely, we obtain the Cave of Winds appeared only in the five-dimensional anti-de Sitter~(AdS) spacetime, and the increasing $z$ hinders not only the condensate but also the appearance of the first-order phase transition. Furthermore, our results agree with the Ginzburg-Landau results near the critical temperature. In addition, the previous AdS superfluid model is generalized to the Lifshitz spacetime.
In the probe limit, we numerically construct a holographic p-wave superfluid model in the 4D and 5D AdS black holes coupled to a Maxwell-complex vector field. We find that, for the condensate with the fixed superfluid velocity, the results are simi
lar to the s-wave cases in both 4D and 5D spacetimes. In particular, The Cave of Winds and the phase transition always being the second order take place in the 5D case. Moreover, we find the second-first order translating point $frac{S_y}{mu}$ increases with the mass squared. Furthermore, for the supercurrent with the fixed temperature, the results agree with the GL prediction near the critical temperature. In addition, this complex vector superfluid model is still a generalization of the SU(2) superfluid model, and also provides a holographic realization of the $He_3$ superfluid system.
