Finite-size scaling analysis of isotropic–polar phase transitions in an amphiphilic fluid

Abstract

We present Monte Carlo simulations of the isotropic-polar (IP) phase transition in an amphiphilic fluid carried out in the isothermal-isobaric ensemble. Our model consists of Lennard-Jones spheres where the attractive part of the potential is modified by an orientation-dependent function. This function gives rise to an angle dependence of the intermolecular attractions corresponding to that characteristic of point dipoles. Our data show a substantial system-size dependence of the dipolar order parameter. We analyze the system-size dependence in terms of the order-parameter distribution and a cumulant involving its first and second moments. The order parameter, its distribution, and susceptibility observe the scaling behavior characteristic of the 3D Ising universality class. Because of this scaling behavior and because all cumulants have a common intersection irrespective of system size we conclude that the IP phase transition is continuous. Considering pressures 1.3 ≤ P ≤ 3.0 we demonstrate that a line of continuous phase transitions exists which is analogous to the Curie line in systems exhibiting a ferroelectric transition. Our results are qualitatively consistent with Landau's theory of continuous phase transitions.

Addendum to ‘Finite-size scaling analysis of isotropic–polar phase transitions in an amphiphilic fluid’

“…As the entries in table 1 reveal, these ratios turn out to be nearly the same for both universality classes. Therefore, use of the correct set of critical exponents affects the plots presented in figures 8-10 of [1] only very marginally as we have verified. Therefore, we conclude that for the present range of system sizes a successful rescaling of quantities such as |m| , χ, or even P N , is insufficient to distinguish between the universality classes of the 3D Ising magnet and the classical 3D Heisenberg fluid.…”

“…Assuming, in addition, hyperscaling to be valid, we can also compute the critical exponent γ . The results summarized in table 1 indicate that our amphiphilic fluid pertains to the universality class of the classical 3D Heisenberg fluid, unlike what we had surmised in our earlier work [1]. However, it turns out that regardless of whether one uses the critical exponents of the 3D Ising universality class or those of the 3D Heisenberg universality class one can rescale |m| , χ, and P(m) such that data obtained for different system sizes collapse onto unique master curves (see figures 8-10 of [1]).…”

“…In [1] we presented a finite-size scaling analysis of the isotropic-polar (IP) phase transition in an anisometric Lennard-Jones bulk fluid. This analysis was based upon the assumption that our model fluid belonged to the universality class of the three-dimensional (D) Ising magnet.…”

“…where N 1 and N 2 are two different particle numbers, t ≡ T/T IP − 1 is a reduced temperature (T IP 1.047 is the temperature at the IP phase transition and a pressure of P = 1.30 in dimensionless units [1]), and β and ν are critical exponents in standard notation. At the critical point (i.e., at t = 0), W 1 (N 1 , N 2 , 0) for different and arbitrary combinations of N 1 and N 2 should have a unique intersection at which the value of W 1 gives the ratio of critical exponents β/ν [2].…”

Ice polyamorphism in the minimal Mercedes-Benz model of water

“…On the other hand, there exist many simple generic models to test the validity of the two-length-scales hypothesis, mostly based on isotropic central potentials 36,[49][50][51][52][53] . Models with anisotropic interactions are far more scarce due to the added complexity imposed by the directional bonds [54][55][56] . In the case of water, however, the strong impact of the directionality of the hydrogen bond on its properties makes the use of isotropic potentials particularly challenging, imposing a fine tuning of the model parameters in order to reproduce the desired properties 57,58 Perhaps the simplest model of water that incorporates a directional bonding scheme was introduced by Ben-Naim in the early 1970s to obtain a qualitative representation of the open hydrogen-bonded network of molecules that makes up liquid water 59,60 .…”