1306.1892 (Dima Bolmatov et al.)

Symmetry breaking gives rise to three states of matter    [PDF]

Dima Bolmatov, Edvard T. Musaev, K. Trachenko

A fundamental task of statistical physics is to start with a microscopic Hamiltonian, predict the system's statistical properties and compare them with observable data. A notable current fundamental challenge is to tell whether and how an interacting Hamiltonian predicts different basic states of matter, including solid, liquid and gas phases. Here, we propose a new idea that enables a unified description of all three states of matter. We introduce a generic form of an interacting phonon Hamiltonian with ground state configurations minimising the Higgs-type potential. Symmetry breaking SO(3) to SO(2), from the group of rotations in reciprocal space to its subgroup, leads to emergence of energy gaps of shear excitations as a consequence of the Goldstone theorem, and readily results in the emergence of all three states of matter.

View original: http://arxiv.org/abs/1306.1892