Exact analysis of phase transitions in mean-field Potts models

Lorenzoni, Paolo and Moro, Antonio (2019) Exact analysis of phase transitions in mean-field Potts models. Physical Review E, 100 (2). 022103. ISSN 2470-0045

Lorenzoni_Moro_revised_final.pdf - Accepted Version

Download (841kB) | Preview
Official URL: https://doi.org/10.1103/physreve.100.022103


We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free energy, in the thermodynamic limit, follows from its semiclassical limit. Analysis of singularities of the equations of state reveals the occurrence of phase transitions of nematic type at not zero external fields and allows for an interpretation of the phase transitions in terms of shock dynamics in the space of thermodynamic variables. The approach is shown at work in the case of a q-state model for q = 3 but the method generalizes to arbitrary q. Critical asymptotics of magnetization, susceptibility, specific heat and relative critical exponents β, γ,and α are also provided.

Item Type: Article
Subjects: F300 Physics
Depositing User: Elena Carlaw
Date Deposited: 23 Aug 2019 12:54
Last Modified: 01 Aug 2021 10:37
URI: http://nrl.northumbria.ac.uk/id/eprint/40444

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics