V. Chelnokov

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

Abstract 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 α derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle.

Phase structure of 3D Z(N) lattice gauge theories at finite temperature

We perform a numerical study of the phase transitions in three-dimensional Z(N) lattice gauge theories at finite temperature for N>4. Using the dual formulation of the models and a cluster algorithm we locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices, compute the average action and the specific heat. Our results are consistent with the two transitions being of infinite order. Furthermore, they belong to the universality class of two-dimensional Z(N) vector spin models.

Deconfinement and universality in the 3D U(1) lattice gauge theory at finite temperature: study in the dual formulation

A bstractWe study analytically and numerically the three-dimensional U(1) lattice gauge theory at finite temperature in the dual formulation. For an appropriate disorder operator, we obtain the renormalization group equations describing the critical behavior of the model in the vicinity of the deconfinement phase transition. These equations are used to check the validity of the Svetitsky-Yaffe conjecture regarding the critical behavior of the lattice U(1) model. Furthermore, we perform numerical simulations of the model for Nt = 1, 2, 4, 8 and compute, by a cluster algorithm, the dual correlation functions and the corresponding second moment correlation length. In this way we locate the position of the critical point and calculate critical indices.

Twist free energy and critical behavior of 3D U(1) LGT at finite temperature

Abstract The twist free energy is computed in the Villain formulation of the 3 D U ( 1 ) lattice gauge theory at finite temperature. This enables us to obtain renormalization group equations describing a critical behavior of the model in the vicinity of the deconfinement phase transition. These equations are used to check the validity of the Svetitsky–Yaffe conjecture regarding the critical behavior of the lattice U ( 1 ) model. In particular, we calculate the two-point correlation function of the Polyakov loops and determine some critical indices.

Phase structure of 3D Z(N) lattice gauge theories at finite temperature: Large-N and continuum limits

Abstract We study numerically three-dimensional Z ( N ) lattice gauge theories at finite temperature, for N = 5 , 6 , 8 , 12 , 13 and 20 on lattices with temporal extension N t = 2 , 4 , 8 . For each model, we locate phase transition points and determine critical indices. We propose also the scaling of critical points with N. The data obtained enable us to verify the scaling near the continuum limit for the Z ( N ) models at finite temperatures.

Duals of U(N) LGT with staggered fermions

Various approaches to construction of dual formulations of non-abelian lattice gauge theories are reviewed. In the case of U(N) LGT we use a theory of the Weingarten functions to construct a dual formulation. In particular, the dual representations are constructed 1) for pure gauge models in all dimensions, 2) in the strong coupling limit for the models with arbitrary number of flavours and 3) for two-dimensional U(N) QCD with staggered fermions. Applications related to the finite temperature/density QCD are discussed.

Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional non-Abelian spin models.

It is argued that two-dimensional U(N) spin models for any N undergo a BKT-like phase transition, similarly to the famous XY model. This conclusion follows from the Berezinskii-like calculation of the two-point correlation function in U(N) models, approximate renormalization group analysis and numerical investigations of the U(2) model. It is shown, via Monte Carlo simulations, that the universality class of the U(2) model coincides with that of the XY model. Moreover, preliminary numerical results point out that two-dimensional SU(N) spin models with the fundamental and adjoint terms and N > 4 exhibit two phase transitions of BKT type, similarly to Z(N) vector models.It is argued that two-dimensional U(N) spin models for any N undergo a Berezinskii-Kosterlitz-Thouless (BKT)-like phase transition, similarly to the famous XY model. This conclusion follows from the Berezinskii-like calculation of the two-point correlation function in U(N) models, approximate renormalization group analysis, and numerical investigations of the U(2) model. It is shown, via Monte Carlo simulations, that the universality class of the U(2) model coincides with that of the XY model. Moreover, preliminary numerical results point out that two-dimensional SU(N) spin models with the fundamental and adjoint terms and N>4 exhibit two phase transitions of BKT type, similarly to Z(N) vector models.

Critical behavior and continuum scaling of 3D Z(N) lattice gauge theories

Three-dimensional

Phase structure of 3D lattice gauge theories at finite temperature

Z(N)

Phase structure of 3DZ(N) lattice gauge theories at finite temperature

lattice gauge theories are studied numerically at finite temperature for