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arXiv:1711.10946 · Physical review. E

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

Martin Hasenbusch B

Published Jan 16, 2018• 14 citations
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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 a check, also simulations of the spin-$\frac{1}{2}$ Ising model are performed. We find ${f}_{\ensuremath{\sigma}\ensuremath{\sigma}\ensuremath{\epsilon}}=1.051(1)$ and ${f}_{\ensuremath{\epsilon}\ensuremath{\epsilon}\ensuremath{\epsilon}}=1.533(5)$ 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 ${L}^{\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\epsilon}}}$, where $L$ is the linear size of the lattice and ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\epsilon}}$ is the scaling dimension of the leading ${Z}_{2}$-even scalar $\ensuremath{\epsilon}$.

DOI
10.1103/physreve.97.012119

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We simulate the improved (q+1)(q+1)(q+1)-state clock model on the simple-cubic lattice at the critical point on lattices of a linear size up to L=960L=960L=960. We compute operator product expansion coefficients for the three-dimensional XYXYXY universality class. These are compared with highly accurate estimates obtained by using the conformal bootstrap method. We find that the results are consistent.
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