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

TL;DR

This paper introduces a finite-range scaling method to analyze critical points in one-dimensional systems with infinite-range interactions, demonstrated on a long-range Ising model.

Contribution

The paper presents a novel finite-range scaling approach to evaluate critical couplings in long-range interacting systems, with a new exponent based on susceptibility logarithm.

Findings

Successfully identified criticality via zeta function singularity

Applied method to a long-range Ising model with promising results

Provides a practical tool for analyzing infinite-range systems

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.