Specific Features of the Effect of Structural Defects on the Correlation and Interaction of Vortex Excitations in the Nonequilibrium BKT Dynamics of the Two-Dimensional XY Model

• Published in: Journal of experimental and theoretical physics 2020-11, Vol.131 (5), p.768-792
• Main Authors: Prudnikov, V. V., Prudnikov, P. V., Popov, I. S.
• Format: Article
• Language: English
• Subjects: Analysis; Classical and Quantum Gravitation; Disorder; Elementary Particles; Monte Carlo method; Order; Particle and Nuclear Physics; Phase Transition in Condensed System; Physics; Physics and Astronomy; Quantum Field Theory; Relativity Theory; Solid State Physics
• ISSN: 1063-7761; 1090-6509
• DOI: 10.1134/S1063776120110096

A Monte Carlo simulation of the nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a high-temperature initial state. The features of the effect of structural disorder on the time dependence of the correlation length ξ( t ) of the system and the dynamical scaling of the spin-spin autocorrelation function C SS ( t , t w ) are revealed. A direct calculation of the dynamic behavior of the correlation length ξ( t ) of the two-dimensional structurally disordered XY model is carried out, and it is shown that this model, just as the pure model, exhibits a time dependence with a logarithmic correction ξ( t ) ∝ ( t /ln t ) 1/2 , which is associated with the nonequilibrium annihilation of vortices and antivortices in the forming vortex pairs. Based on the analysis of the time dependence of the correlation length ξ( t ) and the magnetization cumulant g 2 ( t ), it is shown that the two-dimensional XY model with the spin concentration p = 0.7 is so close to the spin percolation threshold p c that the influence of the attraction of the percolation fixed point becomes crucial for the relaxation properties of the system. However, the features of the critical dynamics of systems with spin concentrations of p = 0.9 and p = 0.8 are determined by the attraction of the pure fixed point. Temperature and concentration dependences of the Fisher critical exponent η( p , T ) are determined using the scaling properties of the calculated two-time dependence of the spin-spin autocorrelation function C SS ( t , t w ). The scaling functions of the two-time dependence of the spin-spin autocorrelation function C SS ( t , t w ) are calculated using the dynamic dependence of the correlation length ξ( t ) obtained as a result of simulation, and the values of the decay exponents λ C ( p , T ) of the scaling functions in the long-time regime are determined, which are in good agreement with the relation λ C ( p , T ) = 1 + η( p , T ) and prove that the dynamical scaling is realized for the nonequilibrium characteristics of structurally disordered systems.