This repository contains Julia implementations of classical and gauge lattice field theories with explicit sampling, parameter learning, and renormalization-group (RG) flow analysis. The goal is to unify statistical inference and field-theoretic RG methods, demonstrating how coupling constants and effective Hamiltonians can be learned directly from simulated or experimental data.
| Model | Dimension | Description / Key Features |
|---|---|---|
| 1D Ising Model | 1D | Analytical baseline; Metropolis sampling; learning using Pseudolikelihood (PL) and RISE estimators; error-scaling and RG analysis. |
| 2D Schwinger Model | 2D | Gauge + fermion formulation; parameter and RG inference (β, m) via score matching; demonstrates gauge–matter coupling learning. |
| Dual Schwinger Model | 2D | Scalar field representation; RG flow reconstruction and error analysis. |
| 2D Sine-Gordon Model | 2D | Sampling using Metropolis, learning β-functions via score matching; comparison with analytical RG predictions and phase boundary. |
| 2D Wegner’s Ising Gauge Theory (WIGT) | 2D | Link-variable lattice gauge theory; implemented with Metropolis and Cluster algorithms; Wilson-loop and string-tension estimation; various RG blocking schemes. |
| 2D Z₂ Higgs Model | 2D | Coupled matter–gauge system; spontaneous symmetry breaking and confinement; joint sampling of link and matter fields. |
- Demonstrates that models with discrete, continuous or mixed data can be learned directly from Monte Carlo samples and from moments only.
- Recovers known RG fixed points and scaling laws for the learned couplings.
- Extracts string tension from Wilson-loop expectation values, confirming the area-law confinement behavior.
- Establishes error-scaling with sample size, following ( |\hat{K} - K| \propto N^{-1/2} ).
- Connects gauge dualities (Schwinger ↔ Dual Schwinger) with learned coarse-grained couplings along the RG flow.
- Learns new non-perturbative behavior about relevant and irrelevant operators.
Metropolis, Heatbath, and Cluster (Swendsen–Wang / Wolff-type) algorithms are implemented for efficient exploration of the configuration space.
For gauge models, sampling is performed over link variables, while for scalar and spin models, site variables are updated using local or cluster moves.
Coupling constants and effective Hamiltonians are learned directly from sampled data using Pseudolikelihood (PL), and Score Matching estimators.
These estimators minimize analytical loss functions derived from the log-likelihood or score function, allowing parameter reconstruction without explicit partition function evaluation.
Several coarse-graining schemes are implemented — including block-spin transformations, plaquette blocking, and checkerboard mappings — to derive scale-dependent effective couplings.
Learned couplings across RG steps yield RG flows that reproduce analytical results, or show new higher order/non-perturbative effects.
Physical quantities such as plaquette energy, autocorrelation functions, Wilson loops, and string tension are computed to monitor equilibrium and confinement behavior.
Diagnostic tools include error-scaling with sample size, autocorrelation time estimation, and RG fixed-point detection.
Together, these components demonstrate how data-driven learning recovers renormalization behavior, universality, and confinement properties from raw lattice configurations.
This code is provided under a BSD license as part of the Optimization, Inference and Learning for Advanced Networks project, C18014.