A General Solution for Network Models with Pairwise Edge Coupling
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908285699883008 |
|---|---|
| author | Catanzaro, Alessio Patil, Subodh Garlaschelli, Diego |
| author_facet | Catanzaro, Alessio Patil, Subodh Garlaschelli, Diego |
| contents | Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous results obtained for specific interaction structures. We use the Hubbard-Stratonovich transform to show that such higher order models can be decoupled into families of effectively separable random graph models, which might be enhanced with auxiliary, possibly multi-valued, parameters identifying the thermodynamical phase of the system. Moreover, given the diagonalizability of couplings between links, we carry out the full computation of the partition functions and discuss why in some cases they can effectively reduce to the one for the Mean-Field case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A General Solution for Network Models with Pairwise Edge Coupling Catanzaro, Alessio Patil, Subodh Garlaschelli, Diego Statistical Mechanics Data Analysis, Statistics and Probability Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous results obtained for specific interaction structures. We use the Hubbard-Stratonovich transform to show that such higher order models can be decoupled into families of effectively separable random graph models, which might be enhanced with auxiliary, possibly multi-valued, parameters identifying the thermodynamical phase of the system. Moreover, given the diagonalizability of couplings between links, we carry out the full computation of the partition functions and discuss why in some cases they can effectively reduce to the one for the Mean-Field case. |
| title | A General Solution for Network Models with Pairwise Edge Coupling |
| topic | Statistical Mechanics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2503.20805 |