Twist free energy and critical behavior of 3 D <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> LGT at finite temperature

The twist free energy is computed in the Villain formulation of the 3 D <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> 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 <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> model. In particular, we calculate the two-point correlation function of the Polyakov loops and determine some critical indices