Double scaling in tensor models with a quartic interaction
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Bibliographic record
Abstract
A bstract In this paper we identify and analyze in detail the subleading contributions in the 1 /N expansion of random tensors, in the simple case of a quartically interacting model. The leading order for this 1 /N expansion is made of graphs, called melons , which are dual to particular triangulations of the D -dimensional sphere, closely related to the “stacked” triangulations. For D < 6 the subleading behavior is governed by a larger family of graphs, hereafter called cherry trees , which are also dual to the D -dimensional sphere. They can be resummed explicitly through a double scaling limit. In sharp contrast with random matrix models, this double scaling limit is stable. Apart from its unexpected upper critical dimension 6, it displays a singularity at fixed distance from the origin and is clearly the first step in a richer set of yet to be discovered multi-scaling limits.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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