| Fig 5 of (1) | Fig 6 of (1) |
|---|---|
References:
- Results contained in (1) 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:
- ONvars_YZ
- Outputs list of Taylor expansion variables for given truncations. Imported by following files.
- 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.
- 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).
- 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).
- 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).
- 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).