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تسجيل مستخدم جديدLifshitz-like black brane thermodynamics in higher dimensions
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Gravitational backgrounds in d+2 dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in d+1 dimensions with critical exponent zgeq 1. We numerically explore a dilaton-Einstein-Maxwell model admitting such backgrounds as solutions. Such backgrounds are characterized by a temperature T and chemical potential mu, and we find how to embed these solutions into AdS for a range of values of z and d. We find no thermal instability going from the (Tllmu) to the (Tggmu) regimes, regardless of the dimension, and find that the solutions smoothly interpolate between the Lifshitz-like behaviour and the relativistic AdS-like behaviour. We exploit some conserved quantities to find a relationship between the energy density E, entropy density s, and number density n, E=frac{d}{d+1}(Ts+nmu), as is required by the isometries of AdS_{d+2}. Finally, in the (Tllmu) regime the entropy density is found to satisfy a power law s propto c T^{d/z} mu^{(z-1)d/z}, and we numerically explore the dependence of the constant c, a measure of the number of degrees of freedom, on d and z.
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