Mar 8 – 10, 2017
Nordita, Stockholm
Europe/Stockholm timezone

Synchronizing the Markov chain at microscopic times

Mar 10, 2017, 10:15 AM
45m
122:026 (Nordita, Stockholm)

122:026

Nordita, Stockholm

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.

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