Infinite compressibility states in the hierarchical reference theory of fluids. I: Analytical considerations
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Publication:2487788
DOI10.1007/S10955-004-2017-XzbMATH Open1071.82028arXivcond-mat/0308467OpenAlexW2120760257MaRDI QIDQ2487788
Author name not available (Why is that?)
Publication date: 8 August 2005
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/cond-mat/0308467
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