%0 Book Section %1 statphys23_0708 %A Ouchi, K. %A Tsukamoto, N. %A Fujiwara, N. %A Horita, T. %A Fujisaka, H. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K dichotomous dynamical markov noise phase spin statphys23 system topic-3 transition xy %T Dynamics in an anisotropic XY spin system driven by dichotomous Markov noise %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=708 %X 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.

@incollection{statphys23_0708, 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 $\Omega$ 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 $\pm H_0$ 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 \begin{equation} p(\tau) = e^{-\tau / \tau_f}, \end{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., \begin{equation} \dot{s} = s - |s|^2 s + \gamma s^* + F(t), \end{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 \begin{equation} \rho(t) \simeq e^{-t/\bar{\tau}} / \bar{\tau}, \end{equation} where $\bar{\tau}$ denotes an average time of switching processes. In the ``Bloch type switching'' region, on the other hand, $\rho(t)$ is characterized as \begin{equation} \rho(t) \simeq t^{-3/2}. \end{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.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Ouchi, K. and Tsukamoto, N. and Fujiwara, N. and Horita, T. and Fujisaka, H.}, biburl = {https://www.bibsonomy.org/bibtex/24cd77ee030c002755686181729a10ce9/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {1de4f0fd659c4f94c4762d94521b497f}, intrahash = {4cd77ee030c002755686181729a10ce9}, keywords = {dichotomous dynamical markov noise phase spin statphys23 system topic-3 transition xy}, month = {9-13 July}, timestamp = {2007-06-20T10:16:27.000+0200}, title = {Dynamics in an anisotropic XY spin system driven by dichotomous Markov noise}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=708}, year = 2007 }