One of the remarkable features distinguishing particle ensembles with aligned anisotropic interactions from simple matter is the formation of anisotropic structures, in particular string or chain fluids. The phase diagram of such systems can be extremely diverse, as shown below. It also critically depends on properties of the interaction of particles. We show that the string-fluid transition can be associated with the bifurcation of the (isotropic) correlation length, may be used as a fingerprint of this transition. [For further information see link (JCP)]
Ensembles of particles with spherically symmetric repulsive Yukawa interaction and additional dipole-dipole interaction (induced by an externa field) exhibit a versatile phase diagram. This includes several solid-solid phase transitions.
We propose a simple variational appraoch based on the Bogoliubov inequality for determening equilibrium solid phases. This means we minimize the free energy
The variational free energy F' (with respect to a reference system, characterized by the Hamiltonian H0)
is then minimized (global optimization of F) with respect to a set of exogen parameters (anisotropy ξ, hardness of the spherical symmetric core κ, energy scale, particle number density ρ) using a variation over geometric variational parameters (which describe the lattice structure). It turns out that depending on the hardness at least three distinct interaction regimes (called soft, medium and hard) can be found. [for further information see link (JCP)]
