Monte Carlo Simulations of Classical O(2) Model on Nice Tree and Bethe Lattice

The Metropolis Monte Carlo algorithm is applied to a classical O(2) model on nice tree and Bethe lattice. Finite-size scaling theory is applied to estimate the critical temperature. The results show that the continuous symmetry may not be spontaneously broken even if d_f ≥ d_w + 1 where d_f and d_w are the fractal dimension and the dimension of the random walk on the structure respectively or even if the random walk on the structure is transient.