Spin Effects in Quantum Chromodynamics and Recurrence Lattices with Multi-Site Exchanges

TL;DR

This thesis explores spin effects in QCD and recurrence lattices, analyzing phase transitions and magnetic properties in complex systems, and investigates azimuthal asymmetries in heavy flavor production in deep inelastic scattering.

Contribution

It introduces recursive lattice methods to study critical phenomena in spin systems and applies these techniques to QCD-related processes, providing new insights into phase transitions and asymmetries.

Findings

Magnetization curves with plateaus and bifurcations in recurrence models.

Complex phase transition structures in cubic symmetry models.

Azimuthal asymmetries in heavy flavor production are sensitive to charm distributions.

Abstract

In this thesis, we consider some spin effects in QCD and recurrence lattices with multi-site exchanges. Main topic of our manuscript are critical phenomena in spin systems defined on the recurrence lattices. Main tool of our approach is the method of recursive (hierarchical) lattices. We apply the method of dynamical mapping (or recursive lattices) for investigation of magnetic properties of the fluid and solid $^3$He, phase transitions in crystals and macromolecules. First, we analyze the helix-coil phase transition for polypeptides and proteins, and describe an quasi unfolding transition (like the cold denaturation process) for the degree of helicity (the order parameter for macromolecules). Next we consider the recurrent models of $^3$He defined on the square, Husimi and hexagon lattices. Using the method of dynamical mapping, the magnetization curves with plateaus, bifurcation point and one period doubling are obtained. Then we investigate the model with cubic symmetry defined on the Bethe lattice and containing both linear and quadratic spin-spin interactions. The magnetization of the system is calculated, and a complex structure of the phase transitions between the disordered, partially ordered and completely ordered states is observed. In the framework of QCD, we consider the azimuthal asymmetries in heavy flavor production in the lepton-nucleon deep inelastic scattering (DIS). We calculate the azimuthal (or $\phi$-) dependence of the next-to-leading order heavy-quark-initiated contributions to DIS. It is shown that, contrary to the basic gluon-initiated component, the photon-quark scattering mechanism is practically $\cos2\phi$-independent. We investigate the possibility of measuring both nonperturbative (intrinsic) and perturbative (CTEQ, MRST) charm distributions using the $\cos2\phi$ asymmetry.