Cluster pair correlation function of simple fluids: energetic connectivity criteria

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by T.L. Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick like integral equation for a velocity-averaged version of Hill's energetic criterion.Comment: 17 pages, 6 figure

Critical behaviour of the Ising ferromagnet confined in quasi-cylindrical pores: A Monte Carlo study

The critical behaviour of the Ising ferromagnet confined in pores of radius R and length L is studied by means of Monte Carlo computer simulations. Quasi-cylindrical pores are obtained by replicating n-times a triangular lattice disc of radius R, where L = na and a is the spacing between consecutive replications. So, spins placed at the surface of the pores have less nearest-neighbours (NN) as compared to 8 NN for spins in the bulk. These “missing neighbour” effects undergone by surface spins cause a strong suppression of surface ordering, leading to an ordinary surface transition. Also, the effect propagates into the bulk for small tubes (R ≤ 12) and the effective critical temperature of the pores is shifted towards lower values than in the bulk case. By applying the standard finite-size scaling theory, subsequently supported by numerical data, we concluded that data collapse of relevant observables, e.g., magnetization (m), susceptibility, specific heat, etc., can only be observed by comparing simulation results obtained by keeping the aspect ratio C ≡ R/L constant. Also, by extrapolating “effective” R-dependent critical temperatures to the thermodynamic limit (R → ∞, C fixed), we obtained TC(∞) = 6.208(4). As suggested by finite-size scaling arguments, the magnetization is measured at the critical point scales according to |m| TcR β ν ∝ R L 1 2 , where β and ν are the standard exponents for the order parameter and the correlation length, respectively. Furthermore, it is shown that close to criticality the axial correlation length decreases exponentially with the distance. That result is the signature of the formation of (randomly distributed) alternating domains of different magnetization, which can be directly observed by means of snapshot configurations, whose typical length (ξ ) is given by the characteristic length of the exponential decay of correlations. Moreover, we show that at criticality ξ = 0.43(2)R.Instituto de Física de Líquidos y Sistemas BiológicosConsejo Nacional de Investigaciones Científicas y TécnicasComisión de Investigaciones Científicas de la provincia de Buenos Aire

Hyperuniformity on spherical surfaces

9 pags., 8 figs., 1 tab., 1 app.We study and characterize local density fluctuations of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. Indeed, some systems that display disordered hyperuniformity, like the spatial distribution of photoreceptors in avian retina, actually occur on curved surfaces. Here we will focus on the local particle number variance and its dependence on the size of the sampling window (which we take to be a spherical cap) for regular and uniform point distributions, as well as for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole, and charge-charge potentials. We show that the scaling of the local number variance as a function of the window size enables one to characterize hyperuniform and nonhyperuniform point patterns also on spherical surfaces.A.G.M., G.Z., and E.L. acknowledge the support from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie Grant No. 734276. E.L. also acknowledges funding from the Agencia Estatal de Investigación and Fondo Europeo de Desarrollo Regional (FEDER) under Grant No. FIS2017-89361-C3-2-P. S.T. was supported in part by the National Science Foundation under Award No. DMR-1714722