Long-Range Spin Models: Coarsening and Aging

• Applicant: Professor Dr. Wolfhard Janke
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 560547547

The project is designed to explore the nonequilibrium kinetics of long-range interacting systems with Monte Carlo computer simulations. Specifically, we shall consider vector spin models in d=2 dimensions with interactions that decay with distance r algebraically as 1/r^(d+sigma). In a quench protocol one cools a disordered initial state spontaneously to a temperature T_q where ordered low-temperature phases exist in thermal equilibrium. The emerging relaxation process is characterized by domain growth and aging phenomena, which both satisfy dynamical scaling laws. While for domain growth theoretical predictions exist, only little is known for the aging properties. For the long-range Ising model (LRIM) with nonconserved magnetization, one objective of subproject 1 is to clarify how the aging exponent behaves at the crossover sigma=1: Continuously or jump-like as in d=1? Here we will vary T_q systematically. In the limiting case T_q=0, we expect that similar to the growth exponent (which in d=1,2 is independent of sigma) also aging features a peculiar behavior. Answering these questions emerging from our previous LRIM studies has now become promising due to our recent methodological improvements that reduce the needed simulation times significantly by several orders of magnitude. Our new method is also very well suited for studying a critical quench to the critical temperature T_c, which allows us the determination of critical exponents from the short- and long-time relaxation behavior. A related nonequilibrium process, where the cooling below T_c is not done abruptly but with a finite rate, is the Kibble-Zurek mechanism. Here we will pay particular attention to the densities of frozen-in defects which is currently of considerable interest in many different fields. For the LRIM with conserved magnetization M we plan to concentrate in subproject 2 on the "off-critical" case with nonzero M, which corresponds to Ostwald ripening of a binary mixture of solid components, and study the scaling laws of domain growth and aging in dependence of sigma and T_q. Besides comparing the growth exponents with theoretical predictions here we also plan detailed analyses of the microscopic transport processes underlying the nonequilibrium kinetics. In subproject 3 we shall investigate for the first time the nonequilibrium kinetics of the long-range XY model (LRXYM) for which only since recently the equilibrium properties are known with sufficient accuracy. Depending on sigma, the low-temperature phase is either magnetized or of Kosterlitz-Thouless type with topological defects (vortex/antivortex) which renders this model particular challenging. Similar to the LRIM, besides the domain-growth and aging laws we shall also consider a critical quench and the Kibble-Zurek mechanism. In an accompanying subproject 4 on method development several ideas for further algorithmic simplifications shall be implemented and tested for their efficiency.

• DFG Programme: Research Grants