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Lattice Monte Carlo

This section collects the results of Markov Chain Monte Carlo integration of the lattice path integral for the bosonic matrix model with different gauge groups SU(\(N\)) and gauge couplings \(\lambda = g^2 N\).

We study the energy observable \(E\) as a function of the lattice size \(n_t\) and the temperature \(T\) towards the continuum limit.

The code for the data analysis is in this repository.

Simulations

We report results for the following parameters.

Gauge groups:

  • SU(2) and SU(3)

't Hooft couplings:

  • \(\lambda \in [0.5, 1.0, 2.0]\)

Lattice sizes:

  • \(n_t \in [16, 24, 32, 48, 64, 96, 128, 192]\)

Temperatures:

  • \(T \in [0.0025, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4]\)

Results

The Markov Chain Monte Carlo (MCMC) chain for the energy observable at each of the parameters in Simulations is plotted as a function of Molecular Dynamics Time Units (MDTU).

Figures are collected in Energy figures.