Computational Novel Technique of Helical(spiral) Boundary Condition in Mont Carlo Algorithms

In this method we work out computational novel technique of helical(spiral) boundary condition[6] in Mont Carlo simulation[2] and metropolis algorithm[2] in order to delineate and determine correlation between different points of Markov Chain[1] which indeed are different conditions of spin configuration in this simulation method. The helical(spiral) boundary condition, Which is offered by two prestigious scientists, Newman and Barkema[5], is applied instead of periodic boundary condition[6] that is used in the most of Mont Carlo simulations .This project has been done for several crystal lattices(10*10-20*20-50*50,100*100) in critical temperature of phase transition with the use of 1000000 Mont Carlo loops and 3000 related Markov points. Finally, we observe that resultant variation of graph which is according to the Markov Chain growth decreases as exponential function. Although it should be cited that the Binder Coefficient[1] also has been calculated by this nascent method. It leads to the phase transition T=2.3 KT Which is also compatible and concur with the previous methods and experimental results. This new approach is able to be extended to the others models such as XY model, Heisenberg model,and Algorithms like wolf Swendensen-wang[2].