Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

Three-dimensional $Z(N)$ lattice gauge theories at zero temperature are studied for various values of $N$. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized $Z(N)$ model for $N=2,3,4,5,6,8$. Numerical computations are used to simulate vector models for $N=2,3,4,5,6,8,13,20$ for lattices with linear extension up to $L=96$. We locate the critical points of phase transitions and establish their scaling with $N$. The values of the critical indices indicate that the models with $N>4$ belong to the universality class of the three-dimensional $XY$ model. However, the exponent $\alpha$ derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle. We also demonstrate the existence of a rotationally symmetric region within the ordered phase for all $N\geq 5$ at least in the finite volume.Comment: 25 pages, 4 figures, 8 table

The phase transitions in 2D Z(N) vector models for N>4

We investigate both analytically and numerically the renormalization group equations in 2D Z(N) vector models. The position of the critical points of the two phase transitions for N>4 is established and the critical index \nu\ is computed. For N=7, 17 the critical points are located by Monte Carlo simulations and some of the corresponding critical indices are determined. The behavior of the helicity modulus is studied for N=5, 7, 17. Using these and other available Monte Carlo data we discuss the scaling of the critical points with N and some other open theoretical problems.Comment: 19 pages, 8 figures, 10 tables; version to appear on Phys. Rev.

Unveiling SU(3) Flux Tubes At Nonzero Temperature: Electric Fields and Magnetic Currents

We report on the results of measuring the chromoelectric fields in a flux tube created by a static quark-antiquark pair in the finite-temperature SU(3) gauge theory. Below the deconfinement temperature the field behavior is similar to the zero-temperature case. Above the deconfinement temperature the field shape remains the same, but the field values drop when the distance between quark and antiquark increases, thus showing the disappearance of confining potential.Comment: 18 pages, 11 figures. arXiv admin note: text overlap with arXiv:2207.0879

Critical behavior of the compact 3d U(1) gauge theory on isotropic lattices

We report on the computation of the critical point of the deconfinement phase transition, critical indices and the string tension in the compact three dimensional U(1) lattice gauge theory at finite temperatures. The critical indices govern the behavior across the deconfinement phase transition in the pure gauge U(1) model and are generally expected to coincide with the critical indices of the two-dimensional XY model. We studied numerically the U(1) model for N_t=8 on lattices with spatial extension ranging from L=32 to L=256. Our determination of the infinite volume critical point on the lattice with N_t=8 differs substantially from the pseudo-critical coupling at L=32, found earlier in the literature and implicitly assumed as the onset value of the deconfined phase. The critical index $\nu$ computed from the scaling of the pseudo-critical couplings with the extension of the spatial lattice agrees well with the XY value $\nu$=1/2. On the other hand, the index $\eta$ shows large deviation from the expected universal value. The possible reasons of such behavior are discussed in details.Comment: 15 pages, 7 figures; version accepted for publication on J. Stat. Mech

Geological-hydrogeochemical characteristics of a "silver spring" water source (the Lozovy ridge)

Geological and hydrogeological characteristics of the Lozovy ridge (Southern Primorye) are studied, as far as karst phenomena are widely distributed within its boundaries. Water-bearing rocks of the karst water source "Silver Spring" ("Serebryany Klyuch"), which is located near the bottom of the "Bear's fang" ("Medvezhiy klyk") cave, are investigated. It is found that karst rocks are presented by calcite (CaCO[3]), and an accessory mineral is barite (BaSO[4]). It is determined that among the trace elements forming the composition of carbonate water-bearing rocks the maximum concentrations are typical for Sr, Ba, Fe, Al, Za, Mn, Cu, and Ni. Also, the chemical composition of the waters taken from the "Silver Spring" water source is studied. These waters are fresh, hydrocarbonate, calcium, and weakly alkaline. Among the elements of the spring, such elements as Sr, Ba, Fe, Al, Zn, Mn, Cu, and Ni have the maximum concentration. The other elements have concentrations less than 1 [mu]g/l