Speaker
Rogelio Díaz-Méndez
(KTH)
Description
The lack of an equation of motion for classical
discrete-variable models is supplemented with the
introduction of a master equation (ME), governing the
probabilities for a system to be in any particular state.
Thus, the information describing the dynamical evolution of
the local variables in a Markov process can be obtained from
the ME through analytical and numerical techniques.
Available numerical methods capable of simulate ME
stochastic trajectories, however, fail to reproduce the
Markov chain dynamics for very small timescales, i.e. at
times of the order of the elementary relaxation. We overcome
this shortcoming by introducing the Event-Driven Monte Carlo
algorithm (ED), whose scheme allows for the simulation of
the exact real-time dynamics of classical many-body systems
with discrete energy levels [1]. Unlike existing methods,
the ED does not assume any particular statistical
distribution to perform moves or to advance the time, and
thus is a unique tool for the numerical exploration of fast
and ultra-fast dynamical regimes. As a prime example of ED
applications we will discuss preliminary results on the
effects of self-induced fields in the
dynamics of the 2D Ising model. While the cumulative effect
of Eddy currents is wellknown to affect the distribution of
avalanches in Barkhausen noise [2], its numerical study
in Ising-like systems requires access to the short-time spin
dynamics. Using the ED scheme, we couple the diffusion
equation of the induced field to the real-time evolution of
the local magnetization and observe an interesting
phenomenology.
[1] A. Mendoza-Coto, R. Díaz-Méndez and G. Pupillo,
Event-driven Monte Carlo: Exact dynamics at all time scales
for discrete-variable models, Europhysics Letters 114, 5, 2016.
[2] F. Colaiori, G. Durin and S. Zapperi, Eddy current
damping of a moving domain wall: Beyond the quasistatic
approximation, Phys. Rev. B 76, 224416, 2007.
