# Critical exponents and amplitudes of analytical equation of state

## TL;DR

This paper derives relations between critical exponents and amplitudes from an analytical equation of state at the liquid-vapor critical point, linking thermodynamic conditions to phase transition characteristics.

## Contribution

It establishes how an analytical equation of state can describe critical behavior, including exponents and amplitudes, and relates to lattice gas models and density fluctuations.

## Key findings

- Critical exponents can match those of the 2D Ising model.
- Analytical equations of state can incorporate density fluctuations.
- Relations between derivatives and phase equilibrium are confirmed.

## Abstract

The paper analyzes a general case of an equation of state, which is an analytical function at the critical point of the liquid-vapor first order phase transition of pure substance. It is shown that the equality to zero of the first- and second-order partial derivatives of pressure with respect to volume (density) at the critical point is the consequence of the thermodynamic conditions of phase equilibrium. We obtained the relations of critical exponents and amplitudes with parameters of the analytical equation of state. It is shown that the substance with the analytical equation of state can have critical exponents of lattice gas which is equivalent to the two dimensional Ising model. It is shown that the analytical equation of state can take into account the density fluctuations.

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Source: https://tomesphere.com/paper/1702.02226