Holographic Phase Transitions in (2+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2+1)$$\end{document}-Dimensional Black Hole Spacetimes in NMG

In this work, we aim at the question of holographic phase transitions in two-dimensional systems with Lifshitz scaling. We consider the gravity side candidate for a dual description as the black hole solution of new massive gravity (NMG) with Lifshitz scaling. We discuss the effects due to the Lifshitz scaling in the AGGH (Ayon-Beato-Garbarz-Giribet-Hassaïne) solution in comparison with the BTZ (Bañados-Teitelboim-Zanelli) black hole. Likewise, we compute the order parameter and it indicates a second-order phase transition in a (1+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1+1)$$\end{document} dimension Lifshitz boundary.