Fluid Coexistence close to Criticality: Scaling Algorithms for Precise Simulation

Abstract

A novel algorithm is presented that yields precise estimates of coexisting liquid and gas densities, ${\rho }^{\pm }(T)$, from grand canonical Monte Carlo simulations of model fluids near criticality. The algorithm utilizes data for the isothermal minima of the moment ratio $Q_L(T;<\rho {>}_L)$ $\equiv <m^2{>}_L^2/<m^4{>}_L$ in $L$$\times$$...$$\times$$L$ boxes, where $m=\rho -<\rho {>}_L$. When $L$$\to$$\infty$ the minima, $Q_m^{\pm }(T;L)$, tend to zero while their locations, ${\rho }_m^{\pm }(T;L)$, approach ${\rho }^{+}(T)$ and ${\rho }^{-}(T)$. Finite-size scaling relates the ratio {\boldmath $\mathcal{Y}$}$=$$({\rho }_m^{+}-{\rho }_m^{-})/\Delta {\rho }_{\infty }(T)$ {\em universally} to $1/2(Q_m^{+}+Q_m^{-})$, where $\Delta {\rho }_{\infty }$$=$${\rho }^{+}(T)-{\rho }^{-}(T)$ is the desired width of the coexistence curve. Utilizing the exact limiting $(L$$\to$$\infty )$ form, the corresponding scaling function can be generated in recursive steps by fitting overlapping data for three or more box sizes, $L_1$, $L_2$, $...$, $L_n$. Starting at a $T_0$ sufficiently far below $T_c$ and suitably choosing intervals $\Delta T_j$$=$$T_{j+1}-T_j$$>$0 yields $\Delta {\rho }_{\infty }(T_j)$ and precisely locates $T_c$.

References in corpus (1)

• Discretization Dependence of Criticality in Model Fluids: a Hard-core Electrolyte

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