## Simulation of vapour-liquid condensation in dipolar fluids and uniform sampling Monte Carlo algorithms

##### Abstract

This works examines the question whether a vapour-liquid phase transition exists in
systems of particles with purely dipolar interactions, a topic which has been the subject
of a longstanding debate. Monte Carlo simulation results for two modi operandi to
tackle this issue are presented. One approach examines the phase behaviour of
fluids of
charged hard dumbbells (CHD), each made up of two oppositely charged hard spheres
with diameters σ and separation d. In the limit d/σ → 0, and with the temperature
scaled accordingly, the system corresponds to dipolar hard spheres (DHS) while for
larger values of d ionic interactions are dominant. The crossover between ionic and
dipolar regimes is examined and a linear variation of the critical temperature T*c in
dipolar reduced units as a function of d is observed, giving rise to an extrapolated
T*cDHS ≈ 0:15. The second approach focuses on the dipolar Yukawa hard sphere (DYHS)fluid, which is given by a dipolar hard sphere and an attractive isotropic interaction Y
of the Yukawa tail form. In this case, the DHS limit is obtained for Y → 0. It is found
that T*c depends linearly on the isotropic interaction strength Y over a wide range,
coinciding with the results for the CHD model and extrapolating to a similar value
of T*c;DHS. However, with the use of specially adapted biased Monte Carlo techniques
which are highly efficient, it is shown that the linear variation of T*c is violated for very
small values of the Yukawa interaction strength, almost two orders of magnitude smaller
than the characteristic dipolar interaction energy. It is found that phase separation is
not observable beyond a critical value of the Yukawa energy parameter, even though in
thermodynamic and structural terms, the DYHS and DHS systems are very similar. It is
suggested that either some very subtle physics distinguishes the DYHS and DHS systems,
or the observation of a phase transition in DHSs is precluded by finite-size effects. In the
context of phase separation in highly correlated fluids, new flat-histogram Monte Carlo
simulation techniques based on the Wang-Landau algorithm are evaluated and shown
to be useful tools. This work presents a general and unifying framework for deriving
Monte Carlo acceptance rules which facilitate flat histogram sampling. The framework
yields uniform sampling rules for thermodynamic states given either by the mechanically
extensive variables appearing in the Hamiltonian or, equivalently, uniformly sample the
thermodynamic fields which are conjugate to these mechanical variables.