Surface Code Threshold Maps to Non-Unitary CFT Critical Exponents — E8 Intelligence Research

FINDING: Surface code threshold (~0.593%) maps to the 2D random-bond Ising model (RBIM) critical point, whose universality class is governed by a non-unitary conformal field theory (CFT) with specific critical exponents. | MATH: Surface code error threshold \( p_c \approx 0.593\% \) (for phenomenological noise) corresponds to the RBIM phase transition; critical exponents: \(\nu \approx 1.5\) (correlation length), \(\eta \approx 0.25\) (anomalous dimension), \(\beta \approx 0.77\) (order parameter). The RBIM is described by a quenched-disorder Ising CFT with central charge \( c = 0 \) (non-unitary, due to disorder averaging), and the conformal block for 3-point functions in the slit-strip geometry (Kytölä) involves hypergeometric functions \( {}_2F_1(a,b;c;z) \) with specific modular parameters. | CONNECTION: The RBIM critical point is a **self-dual** point under Kramers-Wannier duality, with the duality fixed point at \( p_c \). The critical exponents satisfy hyperscaling \( 2 - \alpha Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com