تقرير
Splitting-merging transitions in tensor-vectors systems in exact large-$N$ limits
| العنوان: | Splitting-merging transitions in tensor-vectors systems in exact large-$N$ limits |
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| المؤلفون: | Sasakura, Naoki |
| سنة النشر: | 2022 |
| المجموعة: | High Energy Physics - Theory |
| مصطلحات موضوعية: | High Energy Physics - Theory |
| الوصف: | Matrix models have phase transitions in which distributions of variables change topologically like the Gross-Witten-Wadia transition. In a recent study, similar splitting-merging behavior of distributions of dynamical variables was observed in a tensor-vectors system by numerical simulations. In this paper, we study the system exactly in some large-$N$ limits, in which the distributions are discrete sets of configurations rather than continuous. We find cascades of first-order phase transitions for fixed tensors, and first- and second-order phase transitions for random tensors, being characterized by breaking patterns of replica symmetries. The system is of interest across three different subjects at least: The splitting dynamics plays essential roles in emergence of classical spacetimes in a tensor model of quantum gravity; The splitting dynamics automatically detects the rank of a tensor in the tensor rank decomposition in data analysis; The system provides a variant of the spherical $p$-spin model for spin glasses with a new non-trivial parameter. We discuss some implications of the results from these perspectives. The results are compared with some numerical simulations to check the large-$N$ convergence and the assumptions made in the analysis. Comment: 27 pages, 13 figures. Some improvements in Section 4 and the last section. A minor change in the title |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevD.106.126016 |
| URL الوصول: | http://arxiv.org/abs/2206.12017 |
| رقم الأكسشن: | edsarx.2206.12017 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevD.106.126016 |
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