Phase transition of a chiral molecular model over the complete graph

This paper presents a mean-field approximation of the two-dimensional lattice chiral molecular model introduced by Lombardo et al., Proc. Natl. Acad. Sci. U. S. A. 106(36), 15131-15135 (2009) and simplified by Cruz-Simbron et al., J. Chem. Phys. 160, 084502 (2024), obtained by defining a chiral system over a complete graph. Using thermodynamic formalism, we derive a closed-form expression for the free energy of the system f_β; we establish its analyticity for all β > 0 and its convexity over an interval depending on the Hamiltonian of the system. Our findings confirm the existence of first- and second-order phase transitions within this mean-field framework, confirming the first-order phase transition previously proposed by Lombardo et al., Proc. Natl. Acad. Sci. U. S. A. 106(36), 15131-15135 (2009) in the mean-field approximation. Furthermore, we construct a comprehensive phase diagram for the proposed model, providing a deeper understanding of its thermodynamic behavior.