Classical critical behavior of spin models with long-range interactions

TL;DR

This paper uses extensive Monte Carlo simulations to confirm classical critical exponents and logarithmic corrections in long-range interacting Ising models across different dimensions, providing new precise estimates of critical couplings.

Contribution

It provides the first estimates of critical couplings in 2D and 3D long-range Ising models and confirms theoretical predictions for critical exponents and correlation decay regimes.

Findings

Confirmed renormalization theory predictions for critical exponents.

Observed logarithmic corrections at the upper critical dimension.

Provided highly accurate critical coupling estimates, especially in 1D, 2D, and 3D.

Abstract

We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for the exponents predicted by renormalization theory for systems in one, two, and three dimensions and accurately observe the predicted logarithmic corrections at the upper critical dimension. We give both theoretical and numerical evidence that above the upper critical dimension the decay of the critical spin-spin correlation function in finite systems consists of two different regimes. For one-dimensional systems our estimates for the critical couplings are more than two orders of magnitude more accurate than existing estimates. In two and three dimensions we give, to our knowledge, the first results for the critical couplings.