References:

• Results contained in Universal location of Yang-Lee edge singularity in classic O⁡(𝑁) universality classes.
• More details are contained in my thesis.
• See also Universal Location of the Yang-Lee Edge Singularity in O⁡(𝑁) Theories for first computation which uses a different method.

Contents:

1. ONvars_YZ

• Outputs list of Taylor expansion variables for given truncations. Imported by following files.

2. ON_YLE_BetaFunctions

• Starting from the $O(\partial^2)$ SDE expressions, computes the simplified 3D flows of Taylor expansion coefficients in the YLE expansion for both $\rho$ and $\phi$ parametrizations.
• Computed locally. Output to file and results are used for later computations.
• Arbitrary d (dimension) beta functions computations/expressions not used.

3. Scaling_sol_solver

• Using flows from ON_YLE_BetaFunctions, computes 3D scaling solutions for desired range of $N$ and regulator scale parameter $\alpha$.
• Determines PMS (principle of minimal sensitivity), $\alpha_{\text{PMS}}$, locations of exponents.
• $\Delta$ PMS location is used determination of critical amplitudes from integrated flows.
• Computed locally. Outputs to file and results are used to determine initial conditions for integrating flows via thermal perturbations at fixed renormalized mass (YLE flow).

4. HPC_YZ_delta

• Integrates $\rho$ flows to compute exponent $\delta$ and ampltidue $B_c$ using corrections to scaling.
• Implemeneted on NCSU's high performance cluster (HPC).

5. HPC_YZ_mcdata_once, HPC_YZ_gamma

• Integrates $\rho$ flows to compute the renormalized mass for various $t>0$ which tunes to vanishing (sufficiently small) extneral field $H \approx 0$ for a following computation of $\gamma$ and $C_2^+$.
• Implemeneted on NCSU's high performance cluster (HPC).

6. HPC_YZ_YLE_R40 (not cleaned up)

• Integrates $\rho$ flows for $t>0$ and renormalized mass $m_R^2 \approx 0$ into the complex plane using a modified set of partially (R) renormalized parameters down to $t=-40$.
• Utilizes a switch to $\phi$ flows (transformed to purely real expressions) which approach YLE fixed point. Extracts relevant YLE location/amplitude parameters.
• Implemeneted on NCSU's high performance cluster (HPC).