Finite-Range Scaling Method to Analyze Systems with Infinite-Range Interactions

Abstract

We propose a new practical method for evaluating the critical coupling constant in one-dimensional long-range interacting systems. We assume a finite-range scaling and define its exponent for the logarithm of the susceptibility. We find criticality in the form of a zeta function singularity. As an example, we present results for a long-range Ising model.

Comments: 6 pages, 4 figures