# Derivation of the Critical Point Scaling Hypothesis Using Thermodynamics Only

## Abstract

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## Funding

## Acknowledgments

## Conflicts of Interest

## References and Notes

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**Figure 1.**(Color online) Qualitative level-curve graph of the entropy $s(e,m)$ in the vicinity of the critical point $e={e}_{c}$ and $m=0$. The dashed (blue) curves are at constant entropy with ${s}_{2}<{s}_{c}<{s}_{1}$. The coexistence curve $e-{e}_{c}\approx -B{\left({m}^{2}\right)}^{\mathsf{\Delta}}$ is the solid (red) line where the isentropic curves end for $e<{e}_{c}$ and the magnetic field vanishes $h=0$. The labels $-{m}_{\mathrm{coex}}$ and ${m}_{\mathrm{coex}}$ represent two coexisting states with the same entropy, energy, temperature, field $h=0$, but different magnetizations $\pm {m}_{\mathrm{coex}}$. Within the coexistence curve there is no surface. The point A is at $(e={e}_{c},m\ne 0)$; point B is at the coexistence curve; and point C at $(e>{e}_{c},m=0$). The dotted (magenta) curve is the critical isothermal ${\beta}_{c}$. Although the figure is meant to be qualitative, the coexistence curve was drawn assuming $B=3$ in dimensionless units, with the exponent $\mathsf{\Delta}=1.36315$, corresponding to the 3D Ising model.

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Romero-Rochín, V. Derivation of the Critical Point Scaling Hypothesis Using Thermodynamics Only. *Entropy* **2020**, *22*, 502.
https://doi.org/10.3390/e22050502

**AMA Style**

Romero-Rochín V. Derivation of the Critical Point Scaling Hypothesis Using Thermodynamics Only. *Entropy*. 2020; 22(5):502.
https://doi.org/10.3390/e22050502

**Chicago/Turabian Style**

Romero-Rochín, Víctor. 2020. "Derivation of the Critical Point Scaling Hypothesis Using Thermodynamics Only" *Entropy* 22, no. 5: 502.
https://doi.org/10.3390/e22050502