Abstract
The dynamics of ferromagnetic systems below their critical temperatures
driven by a periodically oscillating magnetic field
$F(t)$ have been extensively studied both theoretically and
experimentally. It is well known that the systems exhibit two qualitatively
different behaviors depending on the amplitude $h$ and the frequency
$Ømega$ of $F(t)$. The transition between the two phases are often
referred to as the dynamical phase transition (DPT).
\par
It is quite interesting to ask whether DPT is observed under another
kind of applied field, especially random field with bounded
amplitude. The fundamental aim of this presentation is to study the
dynamics of the magnetization with a dichotomous Markov noise (DMN)
$F(t)$ instead of periodically oscillating external field. The DMN is a
random noise taking two values $H_0$ and the probability $p(\tau)$
that $F(t)$ continues to take the identical value $+H_0$ of $-H_0$
longer than time $\tau$ is given by
equation
p(\tau) = e^-/ \tau_f,
equation
where the correlation time of $F(t)$ is equal to $\tau_f /2$.
\par
We consider the anisotropic XY spin system driven by $F(t)$, i.e.,
equation
s = s - |s|^2 s + s^* + F(t),
equation
where the order parameter $s(t)$ is a complex number and $\gamma$ is a
control parameter to characterize the anisotropy of the system. We focus
on the motion from $\Re s(t) > 0$ to $ \Re s(t) < 0$ and vice versa, which is
called the ``switching process''. There are two regions in the
($\gamma$, $H_0$) plane with a fixed $\tau_f$ according to whether the
switching process occurs. Furthermore, the switching
process region is divided into several parts in terms of the switching
time distribution $\rho(t)$. In the ``Ising type switching'' region,
$\rho(t)$ is given by
equation
\rho(t) e^-t/\tau / \tau,
equation
where $\tau$ denotes an average time of switching processes. In the
``Bloch type switching'' region, on the other hand, $\rho(t)$ is
characterized as
equation
\rho(t) t^-3/2.
equation
There is also a region where two types of switching process coexist. We will
investigate how such the distributions are formed. Furthermore, the power
spectrum of $\Re s(t)$ and $\Im s(t)$ will be discussed.
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