title: Linear relaxation in large two-dimensional Ising models.
abstract: Critical dynamics in two-dimension Ising lattices up to 2048×2048 is simulated on field-programmable-gate-array- based computing devices. Linear relaxation times are measured from extremely long Monte Carlo simulations. The longest simulation has 7.1×10(16) spin updates, which would take over 37 years to simulate on a general purpose computer. The linear relaxation time of the Ising lattices is found to follow the dynamic scaling law for correlation lengths as long as 2048. The dynamic exponent z of the system is found to be 2.179(12), which is consistent with previous studies of Ising lattices with shorter correlation lengths. It is also found that Monte Carlo simulations of critical dynamics in Ising lattices larger than 512×512 are very sensitive to the statistical correlations between pseudorandom numbers, making it even more difficult to study such large systems.
authors.affiliation: Department of Physics, Xiamen University, Xiamen, Fujian 361005, China.
authors.forename: Y
authors.initials: Y
authors.lastname: Lin
authors.affiliation: Department of Physics, Xiamen University, Xiamen, Fujian 361005, China.
authors.forename: F
authors.initials: F
authors.lastname: Wang