Taylor expansion of effective Hamiltonians by Monte Carlo simulations with fixed block spins

Monte Carlo simulations with fixed block spins allow the computation of Taylor expansion kernels for effective Hamiltonians. The expansion can be performed around arbitrary block spin configurations (bar phi) and does not suffer from truncation errors. Monte Carlo calculation of the Taylor kernels offers a ready possibility to check whether the effective Hamiltonian has good locality properties in the neighborhood of a given configuration (bar phi) . The method is applied in a renormalization group study of the 2-dimensional critical Ising model. The results show that one has to deal with a “large field problem”, as had been expected from rigorous renormalization group studies.