\(\psi\) is a standing wave centered at a particle. It can only take on discrete, quantized values as integer multiples of whole wavelength around a circle centered at the particle. The weak and strong fields produced by the bounded particle pairs as the result of aligning \(\psi\), are then also discrete fields that can only take on specific values.
Both electric field and gravitational field produced by the temperature particle pairs \((T^{-},\,T^{+})\) work against the rigid integrity of a solid in which they are imbued evenly. The electric field pushes the positive nucleus apart and the gravitational field collapses the rigid lattice.
As temperature increases, both fields increase in discrete hops. The solid lattice collapse suddenly at the next discrete jump in \(\psi\) when the forces that holds the material solid is less than the forces due to increasing temperature. The solid melts at a sharp temperature.
There are then two type of melting, one due to the electric field that spreads the material as the positive nuclei are pushed apart, and the other due to the gravitational field that pulls the material inwards as the atoms are attracted closer by the temperature particle pairs between them.
Because of this discrete jump in field strength, the solid particles/atoms/molecules do not take on zero \(KE\) when the just material begins to melt. This is because melting did not occur exactly when the forces are equal,
\(F_T=F_{lattice}\)
where \(F_T\) is the force due to the fields of \((T^{-},\,T^{+})\) and \(F_{lattice}\) is the force that hold the solid rigid. (An over simplification.) But instead,
\(F_T\gt F_{lattice}\)
In cases where \(F_{lattice}\)s are orientation dependent but close to each other, a number of the lattice forces are overcame at the same time.
Another change in phase with temperature is boiling, where the liquid particles do not, in the limiting case, boil off at zero \(KE\) but some positive \(KE\) values often attributed to the need to break surface tension.
This discrete electric field with increasing temperature may also explain the stepped/discrete increase in the electrical resistance of some material with increasing temperature.
