2003/12/15 by O. V. Patsahan, Patsahan, O. V., I. M. Mryglod +1
Materials Science · Mathematics · Physics and Astronomy · #Critical point (mathematics) #FOS: Physical sciences #Hamiltonian (control theory) #Ising model #Material Dynamics and Properties #Mathematical analysis #Mathematical physics #Mathematics #Physics #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0312372
published in arXiv (Cornell University) (Cornell University) · 14 pages
openalex publication_date 2003/12/15 · arxiv created 2003/12/16 · arxiv updated 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the critical behavior of the systems dominated by Coulombic interaction. For this purpose we used the method of collective variables with a reference system. Starting from the Hamiltonian of the restricted primitive model (RPM), the simplest model of ionic fluids, we obtain the functional of the grand partition function given in terms of the two collective variables: the collective variables ρk and ck describing fluctuations of the total number density and charge density, respectively. As the result of integration over the variables ck, the microscopic based effective Hamiltonian of the RPM at the vicinity of its gas-liquid critical point was constructed. The coefficients of the effective Hamiltonian, describing the density fluctuations nearby the gas-liquid critical point, are analyzed. It is shown that, in spite of the long-range character of the Coulombic potential, the effective interactions appeared at this level of the description have the short-range character. As a result, the effective Hamiltonian obtained for the RPM in the vicinity of the critical point has the form of the Ginzburg-Landau-Wilson Hamiltonian of an Ising-like model in a magnetic field. This confirms the fact that the critical behavior of the RPM nearby the gas-liquid critical point belongs to the universal class of a 3D Ising model.