Critical Exponents of the 3-D Ising Model

We present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on $64^3$, $128^3$, and $256^3$ simple cubic lattices. Our MCRG estimates are $K_{nn}^c=0.221655(1)(1)$ and $ν=0.625(1)$. The FSS results for $K^c$ are consistent with those from MCRG but the value of $ν$ is not. Our best estimate $η= 0.025(6)$ covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimate $ω\approx 0.7$ for the correction-to-scaling exponent. We also present results for the renormalized coupling $g_R$ along the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.

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