In this paper we analyze the phase transition phenomena in Born-Infeld AdS black holes using Ehrenfest's scheme of standard thermodynamics. The critical points are marked by the divergences in the heat capacity. In order to investigate the nature of the phase transition, we analytically check both the Ehrenfest's equations near the critical points. Our analysis reveals that this is indeed a second order phase transition. Finally, we analyze the nature of the phase transition using state space geometry approach. This is found to be compatible with the Ehrenfest's scheme.

In this paper, considering the probe limit, we analytically study the onset of holographic s-wave condensate in the planar Schwarzschild-AdS background. Inspired by various low-energy features of string theory, in the present work we replace the conventional Maxwell action with a (nonlinear) Born-Infeld action which essentially corresponds to the higher-derivative corrections of the gauge fields. Based on a variational method which is commonly known as the Sturm-Liouville eigenvalue problem and considering a nontrivial asymptotic solution for the scalar field, we compute the critical temperature for the s-wave condensation. The results thus obtained analytically agree well with the numerical findings [J. Jing and S. Chen, Phys. Lett. B 686, 68 (2010)]. As a next step, we extend our perturbative technique to compute the order parameter for the condensation. Interestingly, our analytic results are found to be of the same order as the numerical values obtained earlier.

There is a renewed interest in conformal field theories (CFT) on ultrametric spaces (p-adic field and its algebraic extensions) in view of their natural adaptability in the holographic setting. We compute the contributions from the exchange interactions to the four-point correlator of the CFT using Witten diagrams with three-scalar interaction vertex. Together with the contributions from the bulk four-point interaction, the contact term, these provide a complete answer. We remark on the singularity structure in Mellin space, and argue that all these models are analogues of adS 2 /CFT

In this paper we have studied the critical phenomena in higher curvature charged black holes in the anti-de Sitter (AdS) space-time. As an example we have considered the third order Lovelock-Born-Infeld black holes in seven dimensional AdS space-time. We have analytically derived the thermodynamic quantities of the system. Our analysis revealed the onset of a higher order phase transition in the black hole leading to an infinite discontinuity in the specific heat at constant charge at the critical points. Our entire analysis is based on the canonical framework where we have fixed the charge of the black hole. In an attempt to study the behaviour of the thermodynamic quantities near the critical points, we have derived the critical exponents of the system explicitly. Although, the values of the critical points have been determined numerically, the critical exponents are calculated analytically. Our results fit well with the thermodynamic scaling laws. The scaling hypothesis is also seen to be consistent with these scaling laws. We find that all types of AdS black holes, studied so far, indeed belong to the same universality class. Moreover, these results are consistent with the mean field theory approximation. We have also derived the suggestive values of the other two critical exponents associated with the correlation function and correlation length on the critical surface. * arindam.lala@bose.res.in arXiv:1205.6121v2 [gr-qc]

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