Monte carlo study of lattice gauge theory

Abstract

General formalism & basic concepts of lattice gauge theory, its relation with the statistical physics and physical meaning of the gauge invariant correlation funtion are considered briefly. Main idea of the Monte Carlo procedure is presented and gauge invariant correlation function of the pure gauge system is measured using the Monte Carlo procedure with the gauge group O and I (discrete subgroup of SU(2)). In the result, we observe the first order phase transition at $β_c$ ≫ 2. Comparing with the fact that asymptotic freedom behavior begins from $β\rightleftarrows2$ for the gauge group SU(2), we conclude that the confinement coexist with the asymptotic freedom for the non-Abelian SU(2) gauge fields on a lattice.