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Convergence of Fine-lattice Discretization for Near-critical Fluids | | Sarvin Moghaddam
; Young C. Kim
; Michael E. Fisher
; | | Date: |
7 Feb 2005 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | University of Maryland | | Abstract: | In simulating continuum model fluids that undergo phase separation and criticality, significant gains in computational efficiency may be had by confining the particles to the sites of a lattice of sufficiently fine spacing, $a_{0}$ (relative to the particle size, say $a$). But a cardinal question, investigated here, then arises, namely: How does the choice of the lattice discretization parameter, $zetaequiv a/a_{0}$, affect the values of interesting parameters, specifically, critical temperature and density, $T_{scriptsize c}$ and $
ho_{scriptsize c}$? Indeed, for small $zeta (lesssim 4 $-$ 8)$ the underlying lattice can strongly influence the thermodynamic properties. A heuristic argument, essentially exact in $d=1$ and $d=2$ dimensions, indicates that for models with hard-core potentials, both $T_{scriptsize c}(zeta)$ and $
ho_{scriptsize c}(zeta)$ should converge to their continuum limits as $1/zeta^{(d+1)/2}$ for $dleq 3$ when $zeta oinfty$; but the behavior of the error is highly erratic for $dgeq 2$. For smoother interaction potentials, the convergence is faster. Exact results for $d=1$ models of van der Waals character confirm this; however, an optimal choice of $zeta$ can improve the rate of convergence by a factor $1/zeta$. For $dgeq 2$ models, the convergence of the {em second virial coefficients} to their continuum limits likewise exhibit erratic behavior which is seen to transfer similarly to $T_{scriptsize c}$ and $
ho_{scriptsize c}$; but this can be used in various ways to enhance convergence and improve extrapolation to $zeta = infty$ as is illustrated using data for the restricted primitive model electrolyte. | | Source: | arXiv, cond-mat/0502169 | | Services: | Forum | Review | PDF | Favorites | |
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