Free Energy Distribution Function of a Random Ising ferromagnet

We study the free energy distribution function of weakly disordered Ising ferromagnet in terms of the D-dimensional random temperature Ginzburg-Landau Hamiltonian. It is shown that besides the usual Gaussian "body" this distribution function exhibits non-Gaussian tails both in the paramagnetic and in the ferromagnetic phases. Explicit asymptotic expressions for these tails are derived. It is demonstrated that the tails are strongly asymmetric: the left tail (for large negative values of the free energy) is much more slow than the right one (for large positive values of the free energy). It is argued that in the critical point the free energy of the random Ising ferromagnet in dimensions D<4 is described by a non-trivial universal distribution function being non self-averagingComment: 10 pages, 2 figure

High-frequency elastic moduli of two-dimensional Yukawa fluids and solids

An approach to calculate high-frequency bulk and shear modului of two-dimensional (2D) weakly screened Yukawa fluids and solids is presented. Elastic moduli are directly related to sound velocities and other important characteristics of the system. In this article we discuss these relations and present exemplary calculation of the longitudinal, transverse, and instantaneous sound velocities and derive a differential equation for the Einstein frequency. Simple analytical results presented demonstrate good accuracy when compared with numerical calculations. The obtained results can be particularly useful in the context of 2D colloidal and complex (dusty) plasma monolayers.Comment: To be published in Phys. Plasma

Self-diffusion in single-component Yukawa fluids

It was suggested in the literature that the self-diffusion coefficient of simple fluids can be approximated as a ratio of the squared thermal velocity of the atoms to the "fluid Einstein frequency," which can thus serve as a rough estimate of the friction (momentum transfer) rate in the dense fluid phase. In this article we test this suggestion using a single-component Yukawa fluid as a reference system. The available simulation data on self-diffusion in Yukawa fluids, complemented with new data for Yukawa melts (Yukawa fluids near the freezing phase transition), are carefully analyzed. It is shown that although not exact, this earlier suggestion nevertheless provides a very sensible way of normalization of the self-diffusion constant. Additionally, we demonstrate that certain quantitative properties of self-diffusion in Yukawa melts are also shared by systems like one-component plasma and liquid metals at freezing, providing support to an emerging dynamical freezing indicator for simple soft matter systems. The obtained results are also briefly discussed in the context of the theory of momentum transfer in complex (dusty) plasmas.Comment: 6 pages, 3 figure

Comment on “Shear modulus of two-dimensional Yukawa or dusty-plasma solids obtained from the viscoelasticity in the liquid state”

In a recent paper [Wang, Huang, and Feng,Phys. Rev. E 99,063206(2019)], Langevin dynamical simulation results related to the shear modulus G of a two-dimensional liquid dusty plasma were reported. The purpose of this Comment is to provide a comparison with available theoretical models to calculate G and to indicate the correct way of interpreting the numerical results

Precursors of order in aggregates of patchy particles

We study computationally the local structure of aggregated systems of patchy particles. By calculating the probability distribution functions of various rotational invariants we can identify the precursors of orientation order in amorphous phase. Surprisingly, the strongest signature of local order is observed for 4-patch particles with tetrahedral symmetry, not for 6-patch particles with the cubic one. This trend is exactly opposite to their known ability to crystallize. We relate this anomaly to the observation that a generic aggregate of patchy systems has coordination number close to 4. Our results also suggest a significant correlation between rotational order in the studied liquids with the corresponding crystalline phases, making this approach potentially useful for a broader range of patchy systems.Comment: 12 pages, 3 figure

Attempted Bethe ansatz solution for one-dimensional directed polymers in random media

We study the statistical properties of one-dimensional directed polymers in a short-range random potential by mapping the replicated problem to a many body quantum boson system with attractive interactions. We find the full set of eigenvalues and eigenfunctions of the many-body system and perform the summation over the entire spectrum of excited states. The analytic continuation of the obtained exact expression for the replica partition function from integer to non-integer replica parameter N turns out to be ambiguous. Performing the analytic continuation simply by assuming that the parameter N can take arbitrary complex values, and going to the thermodynamic limit of the original directed polymer problem, we obtain the explicit universal expression for the probability distribution function of free energy fluctuations.Comment: 32 pages, 1 figur

Three-dimensional structure of a string-fluid complex plasma

Three-dimensional structure of complex (dusty) plasmas was investigated under long-term microgravity conditions in the International-Space-Station-based Plasmakristall-4 facility. The microparticle suspensions were confined in a polarity-switched dc discharge. The experimental results were compared to the results of the molecular dynamics simulations with the interparticle interaction potential represented as a superposition of isotropic Yukawa and anisotropic quadrupole terms. Both simulated and experimental data exhibited qualitatively similar structural features indicating the bulk liquid-like order with the inclusion of solid-like strings aligned with the axial electric field. Individual strings were identified and their size spectrum was calculated. The decay rate of the size spectrum was found to decrease with the enhancement of string-like structural features