Critical percolation in high dimensions Export

@article{citeulike:5954958, abstract = {We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4–13 dimensions. For d < 6 they are preliminary; for d > \~{}6 they are between 20 and 10 4 times more precise than the best previous estimates. This was achieved by three ingredients: (i) simple and fast hashing that allowed us to simulate clusters of millions of sites on computers with less than 500 Mbytes memory; (ii) a histogram method that allowed us to obtain information for several p values from a single simulation; and (iii) a variance reduction technique that is especially efficient at high dimensions where it reduces error bars by a factor of up to ≈30 and more. Based on these data we propose a scaling law for finite cluster size corrections.}, author = {Grassberger, Peter}, citeulike-article-id = {5954958}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.67.036101}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRE/v67/i3/e036101}, citeulike-linkout-2 = {http://link.aps.org/pdf/PRE/v67/i3/e036101}, doi = {10.1103/PhysRevE.67.036101}, journal = {Physical Review E}, keywords = {algorithms, percolation, phase\_transition}, month = {Mar}, number = {3}, pages = {036101+}, posted-at = {2009-10-16 23:37:48}, priority = {2}, publisher = {American Physical Society}, title = {Critical percolation in high dimensions}, url = {http://dx.doi.org/10.1103/PhysRevE.67.036101}, volume = {67}, year = {2003} }

TY - JOUR ID - citeulike:5954958 L3 - citeulike-article-id:5954958 N2 - We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4–13 dimensions. For d < 6 they are preliminary; for d > ~6 they are between 20 and 10 4 times more precise than the best previous estimates. This was achieved by three ingredients: (i) simple and fast hashing that allowed us to simulate clusters of millions of sites on computers with less than 500 Mbytes memory; (ii) a histogram method that allowed us to obtain information for several p values from a single simulation; and (iii) a variance reduction technique that is especially efficient at high dimensions where it reduces error bars by a factor of up to ≈30 and more. Based on these data we propose a scaling law for finite cluster size corrections. IS - 3 JF - Physical Review E TI - Critical percolation in high dimensions PB - American Physical Society VL - 67 SP - 036101 KW - algorithms KW - percolation KW - phase_transition AU - Grassberger, Peter PY - 2003/Mar// UR - http://dx.doi.org/10.1103/PhysRevE.67.036101 ER -