Infinite compressibility states in the Hierarchical Reference Theory of fluids. I. Analytical considerations

Details Infinite compressibility states in the Hierarchical Reference Theory of fluids. I. Analytical considerations Infinite compressibility states in the Hierarchical Reference Theory of fluids. I. Analytical considerations

2003-08-23

arxiv.org/abs/cond-mat/0308467v4

J. Stat. Phys. 118 (2005) 1107-1127

Physics

Condensed Matter

Statistical Mechanics

J. Stat. Phys., in press. Minor changes to match the published version

Scientific paper

10.1007/s10955-004-2017-x

In its customary formulation for one-component fluids, the Hierarchical Reference Theory yields a quasilinear partial differential equation for an auxiliary quantity f that can be solved even arbitrarily close to the critical point, reproduces non-trivial scaling laws at the critical singularity, and directly locates the binodal without the need for a Maxwell construction. In the present contribution we present a systematic exploration of the possible types of behavior of the PDE for thermodynamic states of diverging isothermal compressibility kappa[T] as the renormalization group theoretical momentum cutoff approaches zero. By purely analytical means we identify three classes of asymptotic solutions compatible with infinite kappa[T], characterized by uniform or slowly varying bounds on the curvature of f, by monotonicity of the build-up of diverging kappa[T], and by stiffness of the PDE in part of its domain, respectively. These scenarios are analzyed and discussed with respect to their numerical properties. A seeming contradiction between two of these alternatives and an asymptotic solution derived earlier [Parola et al., Phys. Rev. E 48, 3321 (1993)] is easily resolved.

Affiliated with

Also associated with

No associations

Rating

Infinite compressibility states in the Hierarchical Reference Theory of fluids. I. Analytical considerations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Infinite compressibility states in the Hierarchical Reference Theory of fluids. I. Analytical considerations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinite compressibility states in the Hierarchical Reference Theory of fluids. I. Analytical considerations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-248719