Finite-size scaling of the 5D Ising model

Abstract

We address the long-standing disagreement between renormalization group (RG) and Monte Carlo (MC) study of finite-size scaling for the order parameter distribution function of the 5D Ising model. MC study finds disagreement between the RG and MC on the fourth-order Binder cumulant. Two new results are presented here. First, we compare the RG predictions for the first and third absolute moment to MC data. Good agreement and finite-size corrections which are much smaller than for the cumulant are found. Second, we observe that the size dependence of the corrections is consistent with the RG square-root law, which is slow. This, together with a large correction amplitude for the cumulant, provide a possible explanation for prior disagreement.