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arXiv · 1711.10946

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

Martin Hasenbusch
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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 $f_{σσε} = 1.051(1)$ and $f_{εεε} =1.533(5)$ 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 $L^{-Δ_ε}$, where $L$ is the linear size of the lattice and $Δ_ε$ is the scaling dimension of the leading $Z_2$-even scalar $ε$.

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Martin Hasenbusch. 2017-11-29. Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel model. https://doi.org/10.1103/physreve.97.012119

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