Speaker
Description
The Kibble mechanism plays a prominent role in the theory of the early Universe, as an explanation of the possible formation of cosmic strings. Zurek suggested the analogous effect in liquid helium under rapid cooling, and he conjectured, together with del Campo and Kibble, a scaling-law for the relation between the density of remnant topological defects and the cooling rate, when a system passes through its critical temperature. Such scaling-laws has been observed in many condensed matter experiments.
We examine the validity of Zurek’s scaling law within an alternative framework by numerically investigating the Ising model in one, two, and three dimensions under rapid cooling protocols. Our analysis focuses on the evolution of domain walls throughout the quench process down to zero temperature. For several Markov chain Monte Carlo algorithms, we consistently observe scaling-laws like Zurek’s conjecture, in all dimensions under consideration, which shows that this feature holds more generally than expected.
It is highly remarkable that even the exponents of these scaling-laws are consistent for different algorithms, which hints at a physical meaning regarding the relaxation time of systems in the Ising universality class. This work presents an improved computation-time study of simulations for the 2d Ising model out of equilibrium, examining domain evolution dynamics during cooling processes for two Monte Carlo algorithms.
| Keyword-1 | Topological defects analogues |
|---|---|
| Keyword-2 | Out-of-equilibrium evolution |
| Keyword-3 | Kibble-Zurek mechanism |