Fluid coexistence close to criticality: scaling algorithms for precise simulation Export

@article{citeulike:5445016, abstract = {A novel algorithm is presented that yields precise estimates of coexisting liquid and gas densities, ρ ± ( T ) , from grand canonical Monte Carlo simulations of model fluids near criticality. The algorithm utilizes data for the isothermal minima of the moment ratio inlMMLBox in L × × L boxes, where m = ρ − ρ L . When L →∞ the minima, inlMMLBox , tend to zero while their locations, inlMMLBox , approach ρ + ( T ) and ρ − ( T ) . Finite-size scaling relates the ratio inlMMLBox universally to inlMMLBox , where Δ ρ ∞ = ρ + ( T )− ρ − ( T ) is the desired width of the coexistence curve. Utilizing the exact limiting ( L →∞) 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 Δ T j = T j +1 − T j >0 yields Δ ρ ∞ ( T j ) and precisely locates T c . The algorithm has been applied to simulation data for a hard-core square-well fluid and the restricted primitive model electrolyte for sizes up to inlMMLBox (where a is the hard-core diameter): the coexistence curves can be computed to a precision of ±1–2\% of ρ c up to | T − T c |/ T c =10 −4 and 10 −3 , respectively. Universality of the scaling functions and the exponent β is verified and the ( T c , ρ c ) estimates confirm previous values based on data from above T c . The algorithm extends directly to calculating the diameter, inlMMLBox , and can lead to estimates of the Yang-Yang ratio. Furthermore, a new, explicit approximant for the basic scaling function inlMMLBox permits straightforward estimates of Δ ρ ∞ ( T ) from limited Q -data when Ising-type criticality may be assumed.}, author = {Kim, Y. and Fisher, M.}, citeulike-article-id = {5445016}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.cpc.2005.03.066}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0010465505001633}, day = {01}, doi = {10.1016/j.cpc.2005.03.066}, issn = {00104655}, journal = {Computer Physics Communications}, keywords = {criticality, diameter}, month = {July}, number = {1-3}, pages = {295--300}, posted-at = {2009-08-16 08:09:35}, priority = {2}, title = {Fluid coexistence close to criticality: scaling algorithms for precise simulation}, url = {http://dx.doi.org/10.1016/j.cpc.2005.03.066}, volume = {169}, year = {2005} }

TY - JOUR ID - citeulike:5445016 L3 - citeulike-article-id:5445016 N2 - A novel algorithm is presented that yields precise estimates of coexisting liquid and gas densities, ρ ± ( T ) , from grand canonical Monte Carlo simulations of model fluids near criticality. The algorithm utilizes data for the isothermal minima of the moment ratio inlMMLBox in L × × L boxes, where m = ρ − ρ L . When L →∞ the minima, inlMMLBox , tend to zero while their locations, inlMMLBox , approach ρ + ( T ) and ρ − ( T ) . Finite-size scaling relates the ratio inlMMLBox universally to inlMMLBox , where Δ ρ ∞ = ρ + ( T )− ρ − ( T ) is the desired width of the coexistence curve. Utilizing the exact limiting ( L →∞) 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 Δ T j = T j +1 − T j >0 yields Δ ρ ∞ ( T j ) and precisely locates T c . The algorithm has been applied to simulation data for a hard-core square-well fluid and the restricted primitive model electrolyte for sizes up to inlMMLBox (where a is the hard-core diameter): the coexistence curves can be computed to a precision of ±1–2% of ρ c up to | T − T c |/ T c =10 −4 and 10 −3 , respectively. Universality of the scaling functions and the exponent β is verified and the ( T c , ρ c ) estimates confirm previous values based on data from above T c . The algorithm extends directly to calculating the diameter, inlMMLBox , and can lead to estimates of the Yang-Yang ratio. Furthermore, a new, explicit approximant for the basic scaling function inlMMLBox permits straightforward estimates of Δ ρ ∞ ( T ) from limited Q -data when Ising-type criticality may be assumed. IS - 1-3 JF - Computer Physics Communications SN - 00104655 EP - 300 TI - Fluid coexistence close to criticality: scaling algorithms for precise simulation VL - 169 SP - 295 KW - criticality KW - diameter AU - Kim, Y AU - Fisher, M PY - 2005/07/01/ UR - http://dx.doi.org/10.1016/j.cpc.2005.03.066 ER -