ISSN 0027-1349, Moscow University Physics Bulletin, 2014, Vol. 69, No. 4, pp. 287–292. © Allerton Press, Inc., 2014. Original Russian Text © V.G. Bornyakov, A.G. Kononenko, 2014, published in Vestnik Moskovskogo Universiteta. Fizika, 2014, No. 4, pp. 14–20. 287 INTRODUCTION In recent works on the collision of heavy ions it has been found that quark–gluon matter is a medium with strong interaction [1]. In [2, 3], it was proposed that the unusual properties of quark–gluon matter, includ- ing a very low ratio of the viscosity to the entropy den- sity, can be explained via the consideration of color- magnetic monopoles. The first works on investigating the role of these degrees of freedom in a quark–gluon medium using lattice methods were described in [5– 11]. In our earlier work [12], we investigated the univer- sality of the properties of thermal monopoles, i.e., their independence of the selection of a lattice action. Studies of Abelian color-magnetic currents at the zero temperature have shown that the density of the infra- red component of the magnetic current for various lat- tice actions changes by ~30% [13]. This means that ultraviolet fluctuations make a contribution to the infrared density and should be suppressed. The partial suppression of these fluctuations was achieved by using an improved action. In [12], we used an improved Simanzik lattice action and compared our results for the density and the other characteristics with the results that were obtained using the Wilson action [7–9, 11]. It was found that for thermal mono- poles universality was satisfied if short-range (ultravi- olet) dipoles were not considered. In this work, we continue to study the properties of thermal monopoles with an improved lattice action in the SU(2) gauge theory with specific attention to changes in the properties of thermal monopoles in the vicinity of the confinement–deconfinement phase transition. Quantitatively exact determination of parameters, such as the density of monopoles and the magnetic coupling constant, is necessary, in particular, to verify the hypothesis that magnetic monopoles weakly interact (compared to electrically charged fluctuations) just above the phase transition, but strongly interact at high temperatures [2]. To eliminate the systematic effects caused by Gribov copies, in this work, we used the same procedure for gauge fixing as was applied in [10–12]. 1. MODELING DETAILS The lattice action we used is written as follows: (1) where β impr = 4/g 2 is the inverse coupling constant, u 0 is the parameter of the additional term, and S pl and S rt are the plaquette and rectangular 1 × 2 loop summands in the action, respectively: (2) The calculations were carried out using an asymmetric lattice with the volume V = L t × and the periodic boundary conditions, where L t = 6 and L s = 48 are the numbers of sites in the time and spatial directions, respectively. The temperature was assigned using the following relationship: (3) S β impr S pl β impr 20 u 0 2 -------- S rt , rt ∑ – = S pl rt , 1 2 - Tr 1 U pl tr , – ( ) , u 0 1 2 - Tr U pl ( ) ( ) 4 . = = L s 3 T 1 aL t ------ , = THEORETICAL AND MATHEMATICAL PHYSICS Thermal Monopoles in the SU(2) Gauge Theory on a Lattice V. G. Bornyakov a, b and A. G. Kononenko c a Institute of High-Energy Physics, pl. Nauki 1, Protvino, Moskovskaya oblast, 142280 Russia b Institute for Theoretical and Experimental Physics, ul. Bol’shaya cheremushkinskaya 25, Moscow, 117218 Russia c Department of Physics, Moscow State University, Moscow, 119991 Russia e-mail: vitaly.bornyakov@ihep.ru, agkono@gmail.com Received January 8, 2014; in final form, March 6, 2014 Abstract—Color-magnetic thermal monopoles in SU(2) lattice gluodynamics with improved Simanzik action were studied. The density of the monopoles, the monopole chemical potential, the cluster susceptibil- ity, and the cluster magnetization were studied. These results were compared with results that were reported elsewhere. Keywords: lattice gauge theories, confinement–deconfinement transition, Abelian color-magnetic mono- poles, Bose–Einstein condensation, maximum Abelian gauge, Gribov copies. DOI: 10.3103/S0027134914040055