n-vicinity method for Ising Model with long-range interaction

TL;DR

This paper extends the n-vicinity method to long-range interaction Ising models, providing theoretical formulas for critical inverse temperatures and validating them against simulations, especially in higher dimensions.

Contribution

The paper generalizes the n-vicinity method to long-range interactions in Ising models, offering new theoretical formulas for critical temperatures.

Findings

Theoretical formulas match simulations better in higher dimensions.

The method accurately estimates critical inverse temperatures.

Good agreement observed between theory and simulation.

Abstract

The previously developed n-vicinity method allows us to calculate accurately critical values of inverse temperatures for Ising models with short-range interaction. We generalize the method to the case of long-range interactions in spin systems and obtain theoretical formulas for the inverse temperatures in terms of the spin interaction constants. The comparison of our theoretical estimates with computer simulations for the two- and three-dimensional Ising models shows that the larger the dimension of the problem the better their agreement.