%0 Book Section %1 statphys23_0662 %A Sausset, F. %A Tarjus, G. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K defects dynamical frustration geometric glass heterogeneities statphys23 topic-9 topological transition %T Geometric frustration and the glass transition: the Lennard-Jones liquid on the hyperbolic plane %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=662 %X Geometric frustration, i.e., an incompatibility between extension of the local order preferred in a liquid and tiling of the whole space, has been proposed as a physical mechanism for explaining the glass transition and the phenomenology of supercooled liquids 1,2. In this work, we check the fundamentals of the frustration-based theoretical scenario by investigating, by MD simulation, what seems to be the simplest yet tractable frustrated liquid model: a Lennard-Jones fluid on a hyperbolic plane. Indeed, the two-dimensional system of disks on a flat (Euclidean) plane is not frustrated because the local hexagonal order can propagate in space to form a triangular lattice. Placing the system in hyperbolic geometry introduces frustration, whose strength is associated with the curvature of the hyperbolic plane. We have generalized the standard MD algorithm (equations of motion and, most importantly, periodic boundary conditions 3) to hyperbolic geometry. This is the first time that such a study is undertaken. It allows an investigation of the dynamic and static properties of the model, both as a function of the temperature (and density) and as a function of the degree of frustration, i.e., the curvature of space. We monitor the dynamics by computing the diffusion constant, the hyperbolic analog of the self intermediate scattering function, and the bond-orientational correlation function. We find that the one-component Lennard-Jones fluid does not crystallize and form a glass on the hyperbolic plane. To relate the slowing down of motion as temperature decreases to microscopic characterizations of the frustration, we have studied the topological defects, point-like disclinations and dislocations, that are present in the liquid. This provides a means to describe the interplay between structure and dynamics and investigate the connection between dynamical heterogeneities and topological defects. 1) D. Nelson, Defects and Geometry in Condensed Matter Physics (Cambridge University Press, Cambridge, 2001).\\ 2) G. Tarjus, S. Kivelson, Z. Nussinov, and P. Viot, J. Phys.: Condensed Matter, 17, (2005); cond-mat/0508267.\\ 3) F. Sausset and G. Tarjus, Periodic boundary conditions on the pseudosphere, cond-mat/0703326.

@incollection{statphys23_0662, abstract = {Geometric frustration, i.e., an incompatibility between extension of the local order preferred in a liquid and tiling of the whole space, has been proposed as a physical mechanism for explaining the glass transition and the phenomenology of supercooled liquids [1,2]. In this work, we check the fundamentals of the frustration-based theoretical scenario by investigating, by MD simulation, what seems to be the simplest yet tractable frustrated liquid model: a Lennard-Jones fluid on a hyperbolic plane. Indeed, the two-dimensional system of disks on a flat (Euclidean) plane is not frustrated because the local hexagonal order can propagate in space to form a triangular lattice. Placing the system in hyperbolic geometry introduces frustration, whose strength is associated with the curvature of the hyperbolic plane. We have generalized the standard MD algorithm (equations of motion and, most importantly, periodic boundary conditions [3]) to hyperbolic geometry. This is the first time that such a study is undertaken. It allows an investigation of the dynamic and static properties of the model, both as a function of the temperature (and density) and as a function of the degree of frustration, i.e., the curvature of space. We monitor the dynamics by computing the diffusion constant, the hyperbolic analog of the self intermediate scattering function, and the bond-orientational correlation function. We find that the one-component Lennard-Jones fluid does not crystallize and form a glass on the hyperbolic plane. To relate the slowing down of motion as temperature decreases to microscopic characterizations of the frustration, we have studied the topological defects, point-like disclinations and dislocations, that are present in the liquid. This provides a means to describe the interplay between structure and dynamics and investigate the connection between dynamical heterogeneities and topological defects. 1) D. Nelson, Defects and Geometry in Condensed Matter Physics (Cambridge University Press, Cambridge, 2001).\\ 2) G. Tarjus, S. Kivelson, Z. Nussinov, and P. Viot, J. Phys.: Condensed Matter, 17, (2005); cond-mat/0508267.\\ 3) F. Sausset and G. Tarjus, Periodic boundary conditions on the pseudosphere, cond-mat/0703326.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Sausset, F. and Tarjus, G.}, biburl = {https://www.bibsonomy.org/bibtex/21b89236447a7a08e19b8c9883e0543ae/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {83003128c207f0a883ed441744113e14}, intrahash = {1b89236447a7a08e19b8c9883e0543ae}, keywords = {defects dynamical frustration geometric glass heterogeneities statphys23 topic-9 topological transition}, month = {9-13 July}, timestamp = {2007-06-20T10:16:26.000+0200}, title = {Geometric frustration and the glass transition: the Lennard-Jones liquid on the hyperbolic plane}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=662}, year = 2007 }