The influence of nontrivial topology on the vacuums of lattice gauge theories and spin systems; Approaches to the study of critical phenomena in lattice field theory

Scientific seminar of the department: Wednesday, November 15, 16:15, K-418

The influence of nontrivial topology on the vacuums of lattice gauge theories and spin systems

Alexey Tanashkin Pacific Quantum Center of the Far Eastern Federal University

The report examines the influence of various methods of inducing nontrivial topology on the vacuums of lattice gauge theories and the ground states of spin systems using several examples. The restructuring of the vacuum of (Abelian) compact electrodynamics and (non-Abelian) Yang-Mills theory with a gauge group SU(3) at zero temperature in 3+1 dimensions in the presence of perfectly conducting parallel plates limiting one of the dimensions of the theory is described. By studying the topological perturbations of compact electrodynamics, Abelian monopoles responsible for the linear confinement of electric charges, it is shown that with a decrease in the distance between the plates, the holding properties of the vacuum weaken, which leads to a phase transition into the phase of deconfining between the plates. In SU(3) Yang-Mills theory, new bound boundary states of gluons and their images in a chromometallic mirror are discussed. The assumption about the presence of similar states for heavy quarks is put forward and justified. The nonlocal Potts spin model on a random lattice is considered as a spin model and its basic states are described. The results obtained are interpreted in the framework of the unsolved Nelson-Erdos-Hadwiger problem on the chromatic number of the plane.

Approaches to the study of critical phenomena in lattice field theory

Nikolay Gerasimenko Pacific Quantum Center of the Far Eastern Federal University

The report is devoted to the results of recent research on the use of neural networks in the field of lattice field theory, as well as current successes in constructing zeros of the large canonical partition function within the framework of the Lee-Yang approach. The Monte Carlo method is a fairly reliable way to perform calculations from the first principles of the theory. However, it has a number of difficulties, such as: sign problem, critical deceleration, statistics, etc. As a result, there is a need to find alternatives, which is what the report is dedicated to.