A General Solution for Network Models with Pairwise Edge Coupling

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Catanzaro, Alessio, Patil, Subodh, Garlaschelli, Diego
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