828 research outputs found
Thermodynamic geometry and complexity of black holes in theories with broken translational invariance
The relationship between thermodynamics and the Lloyd bound on the
holographic complexity for a black hole has been of interest. We consider
dimensional anti-de Sitter black holes with hyperbolic geometry as well as
black holes with momentum relaxation that have a minimum for temperature and
mass. We show that the singular points of the thermodynamic curvature of the
black holes, as thermodynamic systems, correspond to the zero points of the
action and volume complexity at the Lloyd bound. For such black holes with a
single horizon, the complexity of volume and the complexity of action at
minimum mass and minimum temperature are zero, respectively. We show that the
thermodynamic curvature diverges at these minimal values. Because of the
behaviour of action complexity and thermodynamic curvature at minimum
temperature, we propose the action complexity as an order parameter of the
black holes as thermodynamic systems. Also, we derive the critical exponent
related to the thermodynamic curvature in different dimensions.Comment: 14 pages, 10 figure
Marginal -Like Deformation and ModMax Theories in Two Dimensions
Recently, the ModMax theory has been proposed as a unique conformal nonlinear
extension of electrodynamics. We have shown in [1] that this modification can
be reproduced a marginal -like deformation from pure Maxwell theory.
Further, this deformation is solved by using a perturbative approach. In this
letter, we will investigate another ModMax-like deformation for a
two-dimensional (2D) scalar field theory. In this regard, we first find a
marginal -like deformation in two dimensions and then reproduce the
MM-like Lagrangian from a multiple 2D scalar field theory.Comment: 11 pages, improved versio
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