Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models

TL;DR

This paper demonstrates that mean field theory accurately describes long-range spin models in the nonextensive regime, validated through analytical scaling and Monte Carlo simulations, except at the critical point where alpha equals d.

Contribution

It provides evidence that mean field theory is exact for nonextensive long-range spin models, extending previous conjectures to a broader class of magnetic systems.

Findings

Mean field theory agrees with Monte Carlo results in nonextensive regimes.

Scaling laws effectively describe nonextensive thermodynamic behavior.

Agreement breaks down at alpha equal to d.

Abstract

The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also consider the two dimensional antiferromagnetic Ising model with the same type of interactions. The mean field solution and Monte Carlo calculations for the equations of state for these models are compared. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behaviour, both types of calculations show an excellent agreement in all the cases here considered, except for alpha=d. These results allow us to extend to nonextensive magnetic models a previous conjecture which states that the mean field theory is exact for the Ising one.