Simulating Yang-Mills on the lattice

    struct GaugeParm{T,G,N}

Structure containning the parameters of a pure gauge simulation. These are:

• beta: Type T. The bare coupling of the simulation
• c0: Type T. LatticeGPU supports the simulation of gauge actions made of 1x1 Wilson Loops and 2x1 Wilson loops. The parameter c0 defines the coefficient on the simulation of the 1x1 loops. Some common choices are:
  • c0=1: Wilson plaquette action
  • c0=5/3: Tree-level improved Lüscher-Weisz action.
  • c0=3.648: Iwasaki gauge action
• cG: Tuple (T, T). Boundary improvement parameters.
• ng: Int64. Rank of the gauge group.
• Ubnd: Boundary field for SF boundary conditions

    struct YMworkspace{T}

Structure containing memory workspace that is resused by different routines in order to avoid allocating/deallocating time. The parameter T represents the precision of the simulation (i.e. single/double). The structure contains the following components

• GRP: Group being simulated
• ALG: Corresponding Algebra
• PRC: Precision (i.e. T)
• frc1: Algebra field with natural indexing.
• frc2: Algebra field with natural indexing.
• mom: Algebra field with natural indexing.
• U1: Group field with natural indexing.
• cm: Complex field with lexicographic indexing.
• rm: Real field with lexicographic indexing.

    function ztwist(gp::GaugeParm{T,G}, lp::SpaceParm{N,M,B,D}[, ipl])

Returns the twist factor. If a plane index is passed, returns the twist factor as a complex{T}. If this is not provided, returns a tuple, containing the factor of each plane.

function gauge_action(U, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace)

Returns the value of the gauge action for the configuration U. The parameters eta and c0 are taken from the gp structure.

function force_gauge(ymws::YMworkspace, U, gp::GaugeParm, lp::SpaceParm)

Computes the force deriving from an improved action with parameter c0, without the prefactor 1/g0^2, and assign it to the workspace force ymws.frc1

    function randomize!(f, lp::SpaceParm, ymws::YMworkspace)

Given an algebra field with natural indexing, this routine sets the components to random Gaussian distributed values. If SF boundary conditions are used, the force at the boundaries is set to zero.

    function plaquette(U, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace)

Computes the average plaquette for the configuration U.

    struct IntrScheme{N, T}

Integrator for the molecular dynamics.

    leapfrog(::Type{T}, eps, ns)

Leapfrog integrator with eps stepsize and ns steps.

    omf2(::Type{T}, eps, ns)

Second order Omelyan integrator with eps stepsize and ns steps.

    omf4(::Type{T}, eps, ns)

Fourth order Omelyan integrator with eps stepsize and ns steps.

    function MD!(mom, U, int::IntrScheme, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace)

Performs the integration of a molecular dynamics trajectory starting from the momentum field mom and the configuration U according to the integrator described by int.

    function hamiltonian(mom, U, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace)

Returns the Energy $H = \frac{p^2}{2}+S[U]$, where the momenta field is given by mom and the configuration by U.

    HMC!(U, int::IntrScheme, lp::SpaceParm, gp::GaugeParm, ymws::YMworkspace; noacc=false)

Performs a HMC step (molecular dynamics integration and accept/reject step). The configuration U is updated ans function returns the energy violation and if the configuration was accepted in a tuple.