Critical behavior of the Ising model with long range interactions

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of the 2D Ising model with long-range interactions, revealing discrepancies with renormalization group predictions near the regime transition.

Contribution

It provides new numerical insights into the critical phenomena of long-range interacting Ising models, challenging existing theoretical predictions.

Findings

Results near the regime change do not match renormalization group predictions.

The model was simulated for a wide range of interaction parameters and system sizes.

Discrepancies suggest the need for revised theoretical understanding.

Abstract

We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter $\sigma$ and for large sizes. We observe that the results close to the change of regime from intermediate to short range do not agree with the renormalization group predictions.