How to differentiate solid, liquid and gas on the basis of symmetry breaking? [closed]

Question

I want to ask this question how to solid, liquid and gaseous state arises due to the concept of symmetry breaking?

Answer 1

I will differentiate solids from liquids and gases first (which are similar to each other from the symmetry viewpoint) and denote the latter two as fluids.

While going from the fluid to the solid phase there is a first order phase transition. This breaks the translational symmetry in Poincare group to a periodic translational symmetry. In addition rotational symmetry is also broken to rotation by specific angles. You can think of the density and internal energy as the order parameters for this phase transition. Also for solids the n-point correlation functions should be constrained by this broken translational symmetry.

Liquid and gas phases both respect the translational and rotational symmetries which are broken in solids. Their n-point correlators are constrained by similar symmetry principles (though the correlators are different). However they can be distinguished by their density, bulk modulus among other order parameters. For a range of pressure and temperature their phase transition is first order in nature, which becomes second order at the critical pressure and temperature (See the critical point here).

Second order phase transitions can be understood using Landau theory. This nicely models the phase transition as a symmetry breaking problem. Calculation of critical exponents using behaviour of order parameter, response and the response functions allow us to classify all such liquid-gas transitions into different universality classes.

Answer 2

As far as I understand, there is no symmetry breaking in liquid-gas transition, which is thus may coexist. By solid we usually mean a crystal that has well-defined periodicity, unlike the disordered to phases, which have continuous translational symmetry.