We study the machine learning techniques applied to the lattice gauge theory's critical behavior, particularly to the confinement/deconfinement phase transition in the SU(2) and SU(3) gauge theories. ...We find that the neural network, trained on lattice configurations of gauge fields at an unphysical value of the lattice parameters as an input, builds up a gauge-invariant function, and finds correlations with the target observable that is valid in the physical region of the parameter space. In particular, we show that the algorithm may be trained to build up the Polyakov loop which serves an order parameter of the deconfining phase transition. The machine learning techniques can thus be used as a numerical analog of the analytical continuation from easily accessible but physically uninteresting regions of the coupling space to the interesting but potentially not accessible regions.
Roberge–Weiss Transition in the Lee–Yang Approach Rogalev, R. N.; Bornyakov, V. G.; Gerasimeniuk, N. V. ...
Physics of particles and nuclei letters,
06/2023, Letnik:
20, Številka:
3
Journal Article
Recenzirano
Thermodynamic quantities characterizing dense and hot strongly interacting matter have been studied in the lattice regularization of QCD with two flavors in the Lee–Yang approach. It is shown that, ...at high temperatures and taking into account a sufficiently large number of fermionic modes, Lee–Yang zeros in the complex plane of baryon fugacity lie on the negative real semiaxis, which corresponds to the Roberge–Weiss transition. On the line of Lee–Yang zeros, the baryon density and pressure have a gap; it is shown that the baryon density jump is proportional to the density of Lee–Yang zeros. Two methods for calculating baryon number distributions are considered; it is shown that the method based on the asymptotic estimate gives only positive state probabilities with a certain baryon number, as opposed to numerical integration. The importance of experimental measurements of these probabilities to study the issue of achieving thermodynamic equilibrium in nuclear-nuclear collisions is discussed.
We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge theories. We show that feed-forward neural network, trained on the lattice configurations of gauge ...fields as input data, finds correlations with the target observable, which is also true in the critical region where the neural network has not been trained. We have verified that the neural network constructs a gauge-invariant function and this property does not change over the entire range of the parameter space.
Analytic Continuation in Lattice QC2D Begun, A.; Bornyakov, V. G.; Gerasimeniuk, N. V. ...
Physics of particles and nuclei,
07/2021, Letnik:
52, Številka:
4
Journal Article
Recenzirano
We simulate the lattice QC
2
D with
staggered fermionic action at imaginary and real quark chemical potential
at one temperature slightly above
. We apply a few methods to make analytic continuation ...of the quark number density using our numerical results for imaginary
. Comparing the outcome of the analytic continuation procedures with our results at real
we determine the most effective way to make the analytic continuation. We believe this method can be applied to thelattice QCD data.
We study the Roberge-Weiss phase transition numerically. The phase transition is associated with the discontinuities in the quark-number density at specific values of imaginary quark chemical ...potential. We parameterize the quark number density \(\rho_q\) by the polynomial fit function to compute the canonical partition functions. We demonstrate that this approach provides a good framework for analyzing lattice QCD data at finite density and a high temperature. We show numerically that at high temperature, the Lee-Yang zeros lie on the negative real semi-axis provided that the high-quark-number contributions to the grand canonical partition function are taken into account. These Lee-Yang zeros have nonzero linear density, which signals the Roberge-Weiss phase transition. We demonstrate that this density agrees with the quark density discontinuity at the transition line.
We study numerically the dependence of the difference between the longitudinal and transverse gluon propagators, \(\Delta=D_L-D_T\), on the momentum and temperature at \(T\gtrsim T_c\) both in SU(2) ...and SU(3) gluodynamics. It is found that the integral of \(\Delta\) with respect to the 3-momentum is sensitive only to infrared dynamics and shows a substantial correlation with the Polyakov loop. At \(T=T_p\sim 1.2 T_c\) it changes sign giving some evidence that \(T_p\) can serve as a boundary of the postconfinement domain.
We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge theories. We show that feed-forward neural network, trained on the lattice configurations of gauge ...fields as input data, finds correlations with the target observable, which is also true in the critical region where the neural network has not been trained. We have verified that the neural network constructs a gauge-invariant function and this property does not change over the entire range of the parameter space.
We study the machine learning techniques applied to the lattice gauge theory's critical behavior, particularly to the confinement/deconfinement phase transition in the SU(2) and SU(3) gauge theories. ...We find that the neural network, trained on lattice configurations of gauge fields at an unphysical value of the lattice parameters as an input, builds up a gauge-invariant function, and finds correlations with the target observable that is valid in the physical region of the parameter space. In particular, if the algorithm aimed to predict the Polyakov loop as the deconfining order parameter, it builds a trace of the gauge group matrices along a closed loop in the time direction. As a result, the neural network, trained at one unphysical value of the lattice coupling \(\beta\) predicts the order parameter in the whole region of the \(\beta\) values with good precision. We thus demonstrate that the machine learning techniques may be used as a numerical analog of the analytical continuation from easily accessible but physically uninteresting regions of the coupling space to the interesting but potentially not accessible regions.
By considering the example of $SU(2)$ gluodynamics, we check numerically the
idea that the strong correlation of the Polyakov loop with the longitudinal
gluon propagator and related quantities can be ...used to substantially reduce the
finite-volume effects as well as to extrapolate in temperature over the
critical domain.
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