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Critical Behaviour in a Planar Dynamical Triangulation Model with a Boundary | | V. A. Malyshev
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3 Oct 2000 | | Subject: | gr-qc | | Abstract: | We consider a canonical ensemble of dynamical triangulations of a 2-dimensional sphere with a hole where the number $N$ of triangles is fixed. The Gibbs factor is $exp (-mu sum deg v)$ where $deg v$ is the degree of the vertex $v$ in the triangulation $T$. Rigorous proof is presented that the free energy has one singularity, and the behaviour of the length $m$ of the boundary undergoes 3 phases: subcritical $m=O(1)$, supercritical (elongated) with $m$ of order $N$ and critical with $m=O(sqrt{N})$. In the critical point the distribution of $m$ strongly depends on whether the boundary is provided with the coordinate system or not. In the first case $m$ is of order $sqrt{N}$, in the second case $m$ can have order $N^{alpha}$ for any $0 | | Source: | arXiv, gr-qc/0010008 | | Services: | Forum | Review | PDF | Favorites | |
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