# Melting curve

Melting curve

## Empirical "one-phase" rules

### Ross melting rule

The Ross melting rule states (Eq. 4 [4]):

$A = \frac{1}{2} NE(0) - Nk_BT \ln \upsilon - Nk_BT \ln \upsilon_f^*$

where $A$ is the Helmholtz energy function, $N$ is the number of cells, $E(0)$ is the potential at the centre of the cell, $k_B$ is the Boltzmann constant, $T$ is the temperature, $\upsilon$ is the volume of the cell, and $\upsilon_f^*$ is the dimensionless reduced volume in configuration space.

### Khrapak melting criteria

The Khrapak one-phase melting criteria for two dimensional crystals with soft long-ranged interactions is given by (Eq 3 in [5]):

$\frac{C_T}{v_T}\approx 4.3$

where $C_T$ is the transverse sound velocity, and $v_T$ is the thermal velocity.