Phase transition by curvature in three dimensional O(N)O(N) sigma model

Using the effective potential, the large-$N$ nonlinear $O(N)$ sigma model with the curvature coupled term is studied on $S^2\times R^1$. We show that, for the conformally coupled case, the dynamical mass generation of the model in the strong-coupled regime on $R^3$ takes place for any finite scalar curvature (or radius of the $S^2$). If the coupling constant is larger than that of the conformally coupled case, there exist a critical curvature (radius) above (below) which the dynamical mass generation does not take place even in the strong-coupled regime. Below the critical curvature, the mass generation occurs as in the model on $R^3$.Comment: 13pages, REVTeX, Many typos are correcte

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Department of Energy Engineering (Battery Science and Technology)The continuous throng in demand for high energy density rechargeable batteries innovatively drives technological development in cell design as well as electrochemically active materials. In that perspective metal-free batteries consisting of a flowing seawater as a cathode active material were introduced. However, the electrochemical performance of the seawater battery was restrained by NASICON (Na3Zr2Si2PO12) ceramic solid electrolyte. Here, we demonstrate a new class of fibrous nanomat hard-carbon (FNHC) anode/1D (one-dimensional) bucky paper (1DBP) cathode hybrid electrode architecture in seawater battery based on 1D building block-interweaved hetero-nanomat frameworks. Differently from conventional slurry-cast electrodes, exquisitely designed hybrid hetero-nanomat electrodes are fabricated through concurrent dual electrospraying and electrospinning for the anode, vacuum-assisted infiltration for the cathode. HC nanoparticles are closely embedded in the spatially reinforced polymeric nanofiber/CNT hetero-nanomat skeletons that play a crucial role in constructing 3D-bicontinuous ion/electron transport pathways and allow to eliminate heavy metallic aluminum foil current collectors. Eventually the FNHC/1DBP seawater full cell, driven by aforementioned physicochemical uniqueness, shows exceptional improvement in electrochemical performance (Energy density = 693 Wh kg-1), (Power density = 3341 W kg-1) removing strong stereotype of ceramic solid electrolyte, which beyond those achievable with innovative next generation battery technologies.ope