Participating Countries and International organizations:
Armenia, Australia, Austria, Azerbaijan, Belarus, Belgium, Brazil, Bulgaria, Canada, Czech Republic, Denmark, Ecuador, Egypt, Finland, France, Germany, Hungary, India, Iran, Italy, Japan, Mongolia, New Zealand, Poland, Republic of Korea, Romania, Russia, Serbia, Slovakia, Slovenia, South Africa, Spain, Switzerland, Taiwan, Ukraine, United Kingdom, USA, Uzbekistan, Vietnam.

Issues addressed and main goals of research:
Development of analytical and numerical methods for studying complex many-body systems that are of current interest in modern condensed matter physics, the development of mathematical models of these systems and the identification of universal laws on the example of studied models. Analysis of both lattice and field-theory models of equilibrium and non-equilibrium statistical systems and modeling of a wide class of new materials, including nanostructured materials, which are of great practical importance. The concepts of scaling and universality allow one to go beyond the model approach and to apply the results obtained to broad classes of phenomena studied in the physics of condensed matter. Study of a wide range of universal phenomena in complex systems - phase transitions in condensed media and high-energy physics, scaling in (magneto)hydrodynamic turbulence, chemical reactions, percolation, etc. by the methods of quantum field theory including the functional renormalization group. The results obtained will be used in carrying out experimental studies of condensed matter at JINR. It is important to note the markedly growing interdisciplinary nature of research, where condensed matter physics and statistical physics closely intersect with atomic and nuclear physics, particle physics, mathematical physics, astrophysics, and biology.

Expected main results in the current year:

• Development ofnew theoretical models and methods for studying fractal systems using the small-angle scattering technique.
   
  Investigation of magnetocapacitive, magnetoresistive and magneto-piezoelectric effects in smart composite materials.
   
  Development of a theory of the optical Stark effect in monolayer transition metal dichalcogenides with intervalley biexciton involvement and valley selectivity of the effect taken into account.
   
  Modeling of carbon(silicon)-tungsten-hydrogen potentials for the use in numerical molecular dynamics investigation of graphene(silicone)-tungsten layered structures to obtain results for comparison with the proton beam irradiation experiments.
   
  Modeling of a linear spin chain with three-body spin interactions with a density matrix renormalization group numerical method in order to obtain a phase diagram as a function of the interaction parameters.
   
  Ab initio estimation of exchange parameters of a Co-based honeycomb Kitaev magnet BaCo₂(AsO₄)₂, and calculation of the corresponding spin-wave spectrum.
   
  Calculation of magnon spectral line broadening in a honeycomb ferromagnet with Dzyaloshinskii-Moriya interactions.
   
  Development of a microscopic theory of spin excitationsin the electron-doped cuprates within the t-J model by considering the antiferromagnetic (AF) order as a function of doping and comparison of the obtained results with available experiments.
   
  Development of a statistical theory for describing the properties of condensed matter systems with extended defects.
   
  Development ofthe theory of quantum nets accomplishing quantum information processing.
   
  Development ofan approach to self-similar extrapolation of asymptotic series, with applications to condensed mater systems and quantum field theory.
   
• Investigation ofthe manifestation of nonlinear phenomena in the dynamics and IV-characteristics of Josephson junction stacks and Josephson nanostructures with ferromagnetic layers.
   
  Investigation ofthe possibility of enhancing the efficiency of detecting current signals by using the Josephson junction stack.
   
  Investigation ofthe conductivity and mobility of charge carriers in modified graphene structures through a combination of molecular dynamics and Landauer approaches.
   
  Investigationofthe temperature behaviour ofresistivity of nanostructural metallic films based on the disclination concept of grain boundary. Calculation of the Hall mobility as a function of temperature and thickness in these materials.
   
  Investigation within the model of strongly correlated electrons of the influence of short-range nonlocal Coulomb repulsion, experimentally observed in doped cuprates, on the structure of pair correlations and on the superconductivity.
   
  Investigation ofelectronic properties of transition metaldichalcohenides and other types of 2D materials in the presence of 0D and 1D randomly distributed defects with a focus on the influence of the edge and bound states of defects on the transport properties in the hopping and resonant transport regimes.
   
• Construction of integrable models connected to complex hypergeometricfunctions. Construction of mixed recurrence and difference equations for thecorresponding functions appearing in the limiting regime of key deformationparameter b→i for hyperbolic hypergeometric functions.
   
  Systematic investigation of the degeneration of multidimensional elliptichypergeometric integrals to the hyperbolic level with a subsequent reductionto the level of complex hypergeometric functions, which corresponds to thedegeneration of 4d superconformal indices to 3d and 2d supersymmetricpartition functions.
   
  Description of the finite-dimensional behavior of the dimer model onlattices with different geometries under different boundary conditions.Investigation of the entangled states of a complex quantum system withsingle-ion anisotropy.
   
  Construction of the Cayley-Hamilton identities and investigation of thecharacteristic subalgebras for the Quantum Matrix algebras oforthogonal type. 
   
  Investigation of a family of stochastic processes on the one-dimensionalchains with two states in the local vertex by the use of the Hecke typestochastic R-matrices
   
  Construction of a new quasi-oscillator generating set for the quantumgroups U_q(gl_n) and investigation with its help of a series of Gelfand-Zetlin representations.
   
  Calculation of exact cluster densities in the percolation model and loop densities in O(1) dense loop modelson lattices with various boundary conditions.
   
  Constructionand solution ofthe lattice model of lattice paths with partial annihilation.
   
  Description of particle flow statistics in an asymmetric avalanche process.
   
  Determination of non-local correlation functions in the models of branching polymers on the lattice with boundary.
  
  
   
• Study of spontaneous isotropy breaking in a generalized model of helical stochastic magnetic hydrodynamics. Calculations of critical indices and fixed RG points in the two-loop approximation.
   
  Development of computational methods for solving equations of a non-perturbative functional renormalization group.
   
  Study of chemical reactions kinetics in stochastic media with random fluctuations of different types. Construction of effective field models and derivation of renormalization group equations for correlation functions of the density field of chemically active molecules. Calculation of scaling exponents.
   
  Performing three-loop calculations of fixed RG points and scaling indices in directed percolation described by some effective field-theoretic action.
   
  Calculation of the thermodynamic potential and investigation of the superfluid/superconducting phase transition and scaling in SU(N) symmetric equilibrium systems of ultra-cold fermions in the framework of the non-perturbative renormalization group.
   
  Study of the influence of isotropic turbulent medium modelled by the stochastic Navier-Stokes equation on the possibility of the occurrence of self-organized criticality in Hwa-Kardar anisotropic model of a moving sand pile.
   
  Study by means of the functional renormalization group of the infrared asymptotic behaviour of the Kardar-Parisi-Zhang model with spatially quenched random noise that describes random surface growth.
   
  Investigation of the transfer of vector impurities in an anisotropic and helical turbulent medium in the presence of a weak external magnetic field.
   
  Study of the magnetic field effect on the transport properties of inversion symmetric Weyl semimetal heterostructures including normal superconductors and proximity induced superconductivity in Weyl semimetals.
   
  Elaboration of semi-analytical methods for computation of bound states spectral functions in effective meson and quark-meson models by means of non-perturbative renormalization group approach and their further implementation for calculation of decay widths and the study of mass generation mechanisms for light mesons.
   

 Collaboration