Monte Carlo studies of correlation length and hyperscaling in the three-dimensional Ising model

We report extensive Monte Carlo simulations and finite-size scaling analysis of the correlation length (${\xi }_{\mathrm{L}}$) for the spin-spin correlation function and the renormalized coupling (${\mathrm{g}}_{\mathrm{L}}$) of the simple-cubic Ising model with a wide range of lattice sizes (L≤96). New methods of analysis which avoid assumptions related to the correlation length were introduced. The exponents ν and 2-α were estimated from separate analysis of ${\xi }_{\mathrm{L}}$ and ${\mathrm{g}}_{\mathrm{L}}$, respectively. A value of ${\mathrm{\omega }}^{\mathrm{*}}$≊0.001±0.07 for the Fisher exponent is obtained. This is consistent with a very small or no violations of hyperscalings.