We propose a new family of mapped WENO schemes by using several adaptive control functions and smoothing approximation the signum function. The proposed introduce adaptivity admit an extensive permitted range parameters in mapping functions. Consequently, they have capacity to achieve optimal convergence rates, even near critical points. Particularly, one these with fine-tuned illustrates signi...

The Fortuin-Kasteleyn (FK) random cluster model, which can be exactly mapped from the $q$-state Potts spin is a correlated bond percolation model. By extensive Monte Carlo simulations, we study FK representation of critical Ising model ($q=2$) on finite complete graph, i.e. mean-field We provide strong numerical evidence that configuration space for $q=2$ contains an asymptotically vanishing se...