Lattice Quantum Field Theory (of Matrix Models)- Final Update Annaba University

We attempt to systematically develop the matrix-model/quantum-theory correspondence by working out explicitly various non-trivial examples.
Fall 2019-2020
Master II, Theoretical Physics, Badji-Mokhtar Annaba University.


-Introductory Remarks:

Path integrals and partition functions, thermal field theory, phase transitions, Monte Carlo methods (only Metropolis algorithm).

-Model I: Vector Models (Ising Model)

Phi-four in two dimensions, the disordered/uniform 2nd order phase transition, Metropolis algorithm, critical behavior in 2 and 4 dimensions, continuum limit and renormalization group equation.

-Model II: Matrix Models (Real Quartic Matrix Model)

The quartic matrix model, the disordered/non-uniform 3rd order phase transition, Metropolis algorithm, multitrace matrix models and noncommutative phi-four, Wigner semi-circle law and emergent geometry.

-Model III: Gauge Models (M-(atrix) Theory)

M-(atrix) theory in large dimension limit, Metropolis algorithm for the coordinates and the holonomy angles,  Hagedorn/deconfinement 2nd order phase transition,  Gross-Witten-Wadia 3rd order phase transition and the emergence of a gap, relation to the black-string/black-hole first order phase transition via gauge/gravity duality.


Simulation I- The Lattice $\Phi_2^4$.
Monte Carlo results: tests_Ising.pdf 
statistical errors: error.f 
random number generators: random.f 
gnuplot script: script
main code: ising.f 
Newton-Raphson method: newton-raphson-phi**4.f 

Simulation II- Quartic Matrix Model: 
Monte Carlo results: tests_multitrace.pdf 
main code: matrix_four.f
eigenvalues sorting: eigen-sorting.f  
eigenvalues histogram: eigen-histogram.f 
Note: Results are obtained by one of our students.

Simulation III- Large number of dimensions of the BFSS Matrix Model:
Monte Carlo results: tests_BFSS.pdf
code without gauge field: matrixQM_v1.f
code with gauge field: matrixQM_v2.f

Background Material

Ising Model 

Lattice QFT (of Matrix Models) 

Phases of gauge theory in lower dimensions and the black-hole/black-string transition  

The multitrace matrix models of noncommutative geometry and quantum gravity  

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