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I will present resent results on the simulation of the two-dimensional LxL Ising model at temperatures below the critical temperature Tc. Using a multimagnetical algorithm it is possible to obtain weights W(M) for all values of the magnetisation M that are inverse proportional to the distribution P(M). During a simulation with these weights, the different values of M are visited in a random-walk like manner. Unexpectedly, this behaviour changes for larger system sizes and lower temperatures and block like structures show up in the time series of the magnetisation. An explanation for this phenomenon was given by [1] who realized that, as a consequence of the periodic boundary conditions of the simulation, the system must perform a transition from droplet to strip configurations (and vice versa) in order to visit all magnetisations. To overcome the barrier that is associated with the transition, we present a new Ansatz, where every phase has its own MUCA weights and a small set of additional weights couple the different phases. As a method to determine in which phase the systems is, an loop update is presented. With typically less than L operations the information about all geometric loop lengths is obtained, given the loop lengths of the last configuration. [1] T. Neuhaus and J. S. Hager, J. Stat. Phys. 113 (2003) 47. |
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