In *arXiv preprint hep-th/ \ldots*, pages 99–117. jan, 1995.

Paper doi abstract bibtex

Paper doi abstract bibtex

We examine the geometrical and topological properties of surfaces surrounding clusters in the 3–\$}d{\$ Ising model. For geometrical clusters at the percolation temperature and Fortuin–Kasteleyn clusters at \$}T{_}c{\$, the number of surfaces of genus \$}g{\$ and area \$}A{\$ behaves as \$}A{\^{}}{\{}x(g){\}}e{\^{}}{\{}-\backslashmu(g)A{\}}{\$, with \$}x{\$ approximately linear in \$}g{\$ and \$}\backslashmu{\$ constant. We observe that cross–sections of spin domain boundaries at \$}T{_}c{\$ decompose into a distribution \$}N(l){\$ of loops of length \$}l{\$ that scales as \$}l{\^{}}{\{}-\backslashtau{\}}{\$ with \$}\backslashtau \backslashsim 2.2{\$. We address the prospects for a string–theoretic description of cluster boundaries. (To appear in proceedings for the Cargese Workshop on "String Theory, Conformal Models and Topological Field Theories", May 1993)

@incollection{Dotsenko1994a, abstract = {We examine the geometrical and topological properties of surfaces surrounding clusters in the 3--{\$}d{\$} Ising model. For geometrical clusters at the percolation temperature and Fortuin--Kasteleyn clusters at {\$}T{\_}c{\$}, the number of surfaces of genus {\$}g{\$} and area {\$}A{\$} behaves as {\$}A{\^{}}{\{}x(g){\}}e{\^{}}{\{}-\backslashmu(g)A{\}}{\$}, with {\$}x{\$} approximately linear in {\$}g{\$} and {\$}\backslashmu{\$} constant. We observe that cross--sections of spin domain boundaries at {\$}T{\_}c{\$} decompose into a distribution {\$}N(l){\$} of loops of length {\$}l{\$} that scales as {\$}l{\^{}}{\{}-\backslashtau{\}}{\$} with {\$}\backslashtau \backslashsim 2.2{\$}. We address the prospects for a string--theoretic description of cluster boundaries. (To appear in proceedings for the Cargese Workshop on "String Theory, Conformal Models and Topological Field Theories", May 1993)}, archivePrefix = {arXiv}, arxivId = {hep-th/9401129}, author = {Dotsenko, Vladimir S. and Picco, Marco and Windey, Paul and Lpthe and Harris, Geoffrey and Marinari, Enzo and Martinec, Emil}, booktitle = {arXiv preprint hep-th/ {\ldots}}, doi = {10.1007/978-1-4615-1819-8_9}, eprint = {9401129}, file = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko, Picco, Windey - 1993 - The Phenomenology of Strings and Clusters in the 3 – d Ising Model.pdf:pdf}, month = {jan}, number = {l}, pages = {99--117}, primaryClass = {hep-th}, title = {{The Phenomenology of Strings and Clusters in the 3-d Ising Model}}, url = {http://arxiv.org/abs/hep-th/9401129 https://doi.org/10.1007/978-1-4615-1819-8{\_}9 http://link.springer.com/10.1007/978-1-4615-1819-8{\_}9}, year = {1995} }

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