Analytical structure of transition matrix in Wang-Landau algorithm
Marina Fadeeva1,2, Lev Barash1,3 and Lev Shchur1,2,3
We investigate presents accuracy and convergence of Wang-Landau (WL)
algorithm. WL algorithm calculates density of states via the random walk.
We use transition matrix (TM) instead of the histogram. We argue that histogram
flatness associated with the stochastic properties of TM. Simulations demonstrate
that the TM goes to the stochastic one when the values of density of states became
closer to the exact values. We use the modification factor f, which scale down as
1/t. Simulation of 1/t-Wang-Landau method and control the accuracy by matrix of
transition demonstrates, that convergence of DoS to the exact value is growing up
as 1/t. The convergence of the density of states can be controlled by the difference
of largest eigenvalue of the matrix from the unity. This give us criteria of accuracy
in estimation of DOS.
The entries of the TM is the probabilities of the transition between energy levels in
Wang-Landau algorithm. We study and compute analytical structure of transition
matrix for 1D Ising model
1
Science Center in Chernogolovka,142432 Chernogolovka, Russia
National Research University Higher School of Economics, 101000 Moscow, Russia
3
Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
2