Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel model

Abstract

We compute two- and three-point functions at criticality for the three-dimensional Ising universality class. To this end we simulate the improved Blume-Capel model at the critical temperature on lattices of a linear size up to $L=1600$. As check also simulations of the spin-1/2 Ising model are performed. We find $f_{\sigma \sigma \epsilon }=1.051(1)$ and $f_{\epsilon \epsilon \epsilon }=1.533(5)$ for operator product expansion coefficients. These results are consistent with but less precise than those recently obtained by using the bootstrap method. An important ingredient in our simulations is a variance reduced estimator of $N$-point functions. Finite size corrections vanish with $L^{-{\Delta }_{\epsilon }}$, where $L$ is the linear size of the lattice and ${\Delta }_{\epsilon }$ is the scaling dimension of the leading $Z_2$-even scalar $\epsilon$.

24 pages, 8 figures

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• Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Sphere
• Bootstrapping the 3d Ising Stress Tensor
• Restoring isotropy in a three-dimensional lattice model: The Ising universality class
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• The Operator Product Expansion for Radial Lattice Quantization of 3D ${\varphi }^4$ Theory