Fermi-Jagla model

The Fermi-Jagla model is a smooth variant of the Jagla model. It is given by (Eq. 1 in ):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r) = \epsilon_0 \left[ \left( \frac{a}{r} \right)^n + \frac{A_0}{1+\exp \left[ \frac{A_1}{A_0} (\frac{r}{a}-A_2) \right]} - \frac{B_0}{1+\exp \left[ \frac{B_1}{B_0} (\frac{r}{a}-B_2) \right]} \right]}

There is a relation between the Fermi function and hyperbolic tangent:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{e^x+1}=\frac{1}{2}-\frac{1}{2}\tanh \frac{x}{2}}

Using this relation one can show that Fermi-Jagla model is equivalent to the generalised Fomin potential (which has scientific priority).

References

Related reading

• Shaina Reisman and Nicolas Giovambattista "Glass and liquid phase diagram of a polyamorphic monatomic system", Journal of Chemical Physics 138 064509 (2013)
• Saki Higuchi, Daiki Kato, Daisuke Awaji, and  Kang Kim "Connecting thermodynamic and dynamical anomalies of water-like liquid-liquid phase transition in the Fermi–Jagla model", Journal of Chemical Physics 148 094507 (2018)