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Article overview
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Fluid Coexistence close to Criticality: Scaling Algorithms for Precise Simulation | | Young C. Kim
; Michael E. Fisher
; | | Date: |
29 Nov 2004 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Abstract: | A novel algorithm is presented that yields precise estimates of coexisting liquid and gas densities, $
ho^{pm}(T)$, from grand canonical Monte Carlo simulations of model fluids near criticality. The algorithm utilizes data for the isothermal minima of the moment ratio $Q_{L}(T;<
ho>_{L})$ $equiv< m^{2}>_{L}^{2}/< m^{4}>_{L}$ in $L$$ imes$$ ...$$ imes$$ L$ boxes, where $m=
ho-<
ho>_{L}$. When $L$$ o$$ infty$ the minima, $Q_{scriptsize m}^{pm}(T;L)$, tend to zero while their locations, $
ho_{scriptsize m}^{pm}(T;L)$, approach $
ho^{+}(T)$ and $
ho^{-}(T)$. Finite-size scaling relates the ratio {oldmath $mathcal Y$}$ = $$(
ho_{scriptsize m}^{+}-
ho_{scriptsize m}^{-})/Delta
ho_{infty}(T)$ {em universally} to ${1/2}(Q_{scriptsize m}^{+}+Q_{scriptsize m}^{-})$, where $Delta
ho_{infty}$$ = $$
ho^{+}(T)-
ho^{-}(T)$ is the desired width of the coexistence curve. Utilizing the exact limiting $(L$$ o $$infty)$ form, the corresponding scaling function can be generated in recursive steps by fitting overlapping data for three or more box sizes, $L_{1}$, $L_{2}$, $...$, $L_{n}$. Starting at a $T_{0}$ sufficiently far below $T_{scriptsize c}$ and suitably choosing intervals $Delta T_{j}$$ = $$T_{j+1}-T_{j}$$ > $0 yields $Delta
ho_{infty}(T_{j})$ and precisely locates $T_{scriptsize c}$. | | Source: | arXiv, cond-mat/0411736 | | Services: | Forum | Review | PDF | Favorites | |
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