A New Measurement of Dynamic Critical exponent of Wolff Algorithm by Dynamic Finite Size Scaling

Abstract

In this work we have calculated the dynamic critical exponent $z$ for 2-, 3- and 4-dimensional Ising models using the Wolff's algorithm through dynamic finite size scaling. We have studied time evolution of the average cluster size, the magnetization and higher moments of the magnetization. It is observed that dynamic scaling is independent of the algorithm. In this sense, universality is established for a wide range of algorithms with their own dynamic critical exponents. For scaling, we have used the literature values of critical exponents to observe the dynamic finite size scaling and to obtain the value of $z$. From the simulation data a very good scaling is observed leading to vanishingly small $z$ values for all three dimensions.