Phase transition in dually weighted colored tensor models |
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Authors: | Dario Benedetti |
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Institution: | a Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Golm, Germany b Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo, Canada |
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Abstract: | Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models with a modified propagator which allows us to associate weight factors to the faces of the graphs, i.e. to the bones (or hinges) of the triangulation, where curvature is concentrated. They correspond to dynamical triangulations in three and higher dimensions with generalized amplitudes. We solve analytically the leading order in 1/N of the most general model in arbitrary dimensions. We then show that a particular model, corresponding to dynamical triangulations with a non-trivial measure factor, undergoes a third-order phase transition in the continuum characterized by a jump in the susceptibility exponent. |
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Keywords: | _method=retrieve& _eid=1-s2 0-S0550321311005748& _mathId=si3 gif& _pii=S0550321311005748& _issn=05503213& _acct=C000069490& _version=1& _userid=6211566& md5=b94c5288f2440bb92c5415fbc53c42f3')" style="cursor:pointer 1/N expansion of random tensor models" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">1/N expansion of random tensor models Critical behavior Dynamical triangulation |
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