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.

Lorenzoni, P., Moro, A. (2019). Exact analysis of phase transitions in mean-field Potts models. PHYSICAL REVIEW. E, 100(2) [10.1103/PhysRevE.100.022103].

Exact analysis of phase transitions in mean-field Potts models

Lorenzoni, P
;
Moro, A
2019

Abstract

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.
Articolo in rivista - Articolo scientifico
mean field model, shock dynamics, phase transitions
English
2019
100
2
022103
none
Lorenzoni, P., Moro, A. (2019). Exact analysis of phase transitions in mean-field Potts models. PHYSICAL REVIEW. E, 100(2) [10.1103/PhysRevE.100.022103].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/259027
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