Universal Amplitude Ratios in the 3D Ising Model

TL;DR

Caselle and Hasenbusch deliver high-precision Monte Carlo estimates of universal amplitude ratios in the 3D Ising model by separately analyzing high- and low-temperature regimes and rigorously controlling finite-size and scaling corrections. They employ state-of-the-art algorithms and direct ratio-based analysis to extract quantities such as $C_+/C_-$, $f_{+,2nd}/f_{-,2nd}$, and $u^*$, yielding results that agree with field theory and series expansions and offering explanations for prior MC discrepancies. The work also contrasts these MC outcomes with an effective potential approach and experimental measurements, highlighting robust universality across theory and experiment and providing a stringent benchmark for future studies. Overall, the paper strengthens the understanding of universal amplitude ratios in the 3D Ising universality class and demonstrates reliable, precise methods for their determination.

Abstract

We present a high precision Monte Carlo study of various universal amplitude ratios of the three dimensional Ising spin model. Using state of the art simulation techniques we studied the model close to criticality in both phases. Great care was taken to control systematic errors due to finite size effects and correction to scaling terms. We obtain $C_+/C_-=4.75(3)$, $f_{+,2nd}/f_{-,2nd}=1.95(2)$ and $u^*=14.3(1)$. Our results are compatible with those obtained by field theoretic methods applied to the $φ^4$ theory and high and low temperature series expansions of the Ising model. The mismatch with a previous Montecarlo study by Ruge et al. remains to be understood.