Effects of the hyperscaling violation and dynamical exponents on the imaginary potential and entropic force of heavy quarkonium via holography

The imaginary potential and entropic force are two important different mechanisms to characterize the dissociation of heavy quarkonia. In this paper, we calculate these two quantities in strongly coupled theories with anisotropic Lifshitz scaling and hyperscaling violation exponent using holographic methods. We study how the results are affected by the hyperscaling violation parameter $$ \theta $$ θ and the dynamical exponent z at finite temperature and chemical potential. Also, we investigate the effect of the chemical potential on these quantities. As a result, we find that both mechanisms show the same results: the thermal width and the dissociation length decrease as the dynamical exponent and chemical potential increase or as the hyperscaling violating parameter decreases.

The superconducting dome for holographic doped Mott insulator with hyperscaling violation

We reconsider the holographic model featuring a superconducting dome on the temperature-doping phase diagram with a modified view on the role of the two charges. The first type charge with density $$\rho _{A}$$ ρ A make the Mott insulator, and the second one with $$\rho _{B}$$ ρ B is the extra charge by doping, so that the complex scalar describing the cooper pair condensation couples only with the second charge. We point out that the key role in creating the dome is played by the three point interaction $$-c \chi ^{2} F_{\mu \nu }G^{\mu \nu }$$ - c χ 2 F μ ν G μ ν . The Tc increases with their coupling. We also consider the effect of the quantum critical point hidden under the dome using the geometry of hyperscaling violation. Our results show that the dome size and optimal temperature increase with z whatever is $$\theta $$ θ , while we get bigger $$\theta $$ θ for larger (smaller) dome depending on $$z>2$$ z > 2 ($$z<2$$ z < 2 ). We also point out that the condensate increases for bigger value of $$\theta $$ θ but for smaller value of z.

Hyperscaling Violation in Ising Spin Glasses

In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D = 6 . Estimates are obtained for the “violation of hyperscaling exponent” values in the various models.