School of Mathematical & Statistical Sciences Faculty Publications
Document Type
Article
Publication Date
1-18-2022
Abstract
We study a log-gas on a network (a finite, simple graph) confined in a bounded subset of a local field (i.e., R, C, and Qp being the field of p-adic numbers). In this gas, a log-Coulomb interaction between two charged particles occurs only when the sites of the particles are connected by an edge of the network. The partition functions of such gases turn out to be a particular class of multivariate local zeta functions attached to the network and a positive test function, which is determined by the confining potential. The methods and results of the theory of local zeta functions allow us to establish that the partition functions admit meromorphic continuations in the parameter β (the inverse of the absolute temperature). We give conditions on the charge distributions and the confining potential such that the meromorphic continuations of the partition functions have a pole at a positive value βUV, which implies the existence of phase transitions at finite temperature. In the case of p-adic fields, the meromorphic continuations of the partition functions are rational functions in the variable p −β . We give an algorithm for computing such rational functions. For this reason, we can consider the p-adic log-Coulomb gases as exact solvable models. We expect that all these models for different local fields share common properties and that they can be described by a uniform theory.
Recommended Citation
Zúñiga-Galindo, Wilson A., Brian A. Zambrano-Luna, and Edwin León-Cardenal. "Graphs, local zeta functions, log-Coulomb gases, and phase transitions at finite temperature." Journal of Mathematical Physics 63, no. 1 (2022). https://doi.org/10.1063/5.0070683
Publication Title
Journal of Mathematical Physics
DOI
10.1063/5.0070683
Comments
Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0070683