Virial coefficients and equation of state of hard-core fluids in d-dimensions
By: Mariano López de Haro
From: Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
At: Complexo Interdisciplinar, Anfiteatro
[2009-05-27]
In this talk I will discuss the convergence properties of the virial series of hard-core fluids in d-dimensions. First, using the results of a recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E. 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick (PY) equation for a fluid of hard spheres in (odd) d dimensions, I will consider the equations of state of these systems derived through the virial and the compressibility routes. In both cases, the virial coefficients bj turn out to be expressed in terms of the solution of a set of (d - 1)/2 coupled algebraic equations which become nonlinear for d ≥ 5 and I will show results derived up to d = 13. These confirm the alternating character of the series of the PY theory for d ≥ 5, due to the existence of a branch point on the negative real axis, which in turn allows one to obtain the corresponding radius of convergence for each dimension. The resulting scaled density per dimension 2η1/d, where η is the packing fraction, is wholly consistent with the limiting value of 1 for d o ∞. Next, using the first seven known (exact) virial coefficients [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)] and forcing it to possess two branch-point singularities, I will introduce a new proposal for the equation of state of hard-core fluids in d-dimensions. For d = 3 this equation of state predicts accurate values of the higher virial coefficients, a radius of convergence smaller than the close-packing value and it is as accurate as the rescaled virial expansion or the Pade [3/3] equations of state. Finally, I will point out some possible consequences regarding the convergence properties of the true virial series.