arXiv:1111.0169v1 [hep-lat] 1 Nov 2011 First study of the abelian monopoles in finite temperature lattice SU (2) gluodynamics with improved action V. G. Bornyakov High Energy Physics Institute, 142280 Protvino, Russia and Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia A. G. Kononenko Joint Institute for Nuclear Research, 141980, Dubna, Russia The properties of the abelian monopoles in the maximally abelian gauge are studied in the vicinity of the phase transition and in the deconfinement phase of the lattice SU (2) gluodynamics. To check universality of the monopole properties we employ the tadpole improved Symanzik action. The simulated annealing algorithm is applied for fixing the maximally abelian gauge to avoid effects of Gribov copies. We measure various quantities characterizing the monopole clusters percolation near to the phase transition. We also compute the density and interaction parameters of the thermal abelian monopoles in the temperature range between Tc and 3Tc. Comparing with earlier results for these quantities obtained with the Wilson action we make conclusions about (in)dependence of the thermal monopole properties on the lattice action. PACS numbers: 11.15.Ha, 12.38.Gc, 12.38.Aw Keywords: Lattice gauge theory, deconfinement phase, thermal monopoles, Gribov problem, simulated an- nealing I. INTRODUCTION The two components model suggested in [1] to ex- plain low ratio η/s property of the quark-gluon matter found in heavy ion collisions experiments requires ex- istence of the condensate of 3d effective scalar field in the deconfinement phase. One candidate for the source of such scalar field are abelian monopoles stud- ied in the past extensively on the lattice both at T =0 and T> 0. The possible important role of monopoles in the quark-gluon phase inspired a number of publications recently [2–9]. It was shown in Ref. [3] that thermal monopoles in Minkowski space are associated with Euclidean monopole trajectories wrapped around the tempera- ture direction of the Euclidean volume. So the den- sity of the monopoles in the Minkowski space is given by the average of the absolute value of the monopole wrapping number. Lattice gauge theory suggests a direct way to study fluctuations contributing to the functional integral. In a number of papers the evidence was found that the nonperturbative properties of the gluodynamics such as confinement, deconfining transition, chiral symme- try breaking, etc. are closely related to the abelian monopoles defined in the maximally Abelian gauge (MAG). This was called a monopole dominance. The drawback of this approach to the monopole studies is that the definition is based on the choice of Abelian gauge. There are various arguments for Abelian monopoles found in MAG to be important physical fluctuations surviving the cutoff removal: monopole density at T=0 is scaling according to dimension 3 (for percolating cluster and for small loops with length above fixed value in physical units); Abelian and monopole dominance for a number of infrared physics observables (string tension, chiral conden- sate); monopoles in MAG are correlated with gauge invariant objects - instantons and calorons. Let us note that in [2] another approach to study monopole properties in the quark-gluon plasma phase based on the molecular dynamics algorithm has been suggested and implemented. Results for parameters of inter-monopole interaction were found in agreement with lattice results [7]. To make results of lattice studies of the monopole properties reliable it is necessary to demonstrate that correct continuum limit exist, Gribov copies effects are negligible, results fo not depend on lattice action discretization (universality). This paper is mainly de- voted to check of universality. We make computations for L t = 4 and compare our results with results ob- tained with Wilson action also for L t = 4 [9]. First numerical investigations of the wrapping monopole trajectories were performed in SU (2) Yang- Mills theory at high temperatures in Refs. [10] and [11]. A more systematic study of the thermal monopoles has been performed in Ref. [6]. It was found in [6] that the density of monopoles is inde- pendent of the lattice spacing, as it should be for a physical quantity. The density–density spatial corre- lation functions has been computed in [6]. It has been shown that there is a repulsive (attractive) interaction for a monopole–monopole (monopole–antimonopole) pair, which at large distances might be described by a screened Coulomb potential with a screening length of the order of 0.1 fm. In [6] the computations were made using relaxation