%0 Book Section %1 statphys23_0042 %A Kim, E. %A Lee, S.J. %A Kim, B. %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 antiferro-ising frustrated model nonequilibrium relaxation statphys23 system topic-3 triangular %T Nonequilibrium relaxation with the ground-state manifold in the antiferromagnetic Ising model on a triangular lattice %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=42 %X We present an extensive Monte Carlo simulation study on the nonequilibrium kinetics of triangular antiferromagnetic Ising model within the ground state ensemble which consists of sectors, each of which is characterized by a unique value of the string density $p$ through a dimer covering method. In our pevious work(PRE 68, 066127(2003)), we considered the nonequilibrium relaxation with dominant sector $p=2/3$ which is the highest entropic state within ground manifold. Here we extended the nonequilibirum kinetics within the minor sectors with $p<2/3$. As a results of the simulations, we observed emergence of a critical relaxation region which grows as $p$ deviated from $p=2/3$. Spatial anisotropy appears in the equilibrium spatial correlation with the characteristic length scale $\xi_e,V(p)$ diverging with vanishing string density as $\xi_e,V(p) p^-2$ along the vertical direction, while along the horizontal direction the spatial length scale diverges as $\xi_e,H(p) p^-1$. Analytic forms for the anisotropic equilibrium correlation functions are give. We also find that the spin autocorrelation function $A(t)$ shows a simple scaling behaviour $A(t)=A(t/\tau_A(p))$, where the time scale $\tau_A(p)$ shows a power-law divergence with vanishing p as $\tau_A(p)p^-\phi$ with $4$. These features can be understood in terms of random walk nature of the fluctuation of the strings within the typical separation between neighbouring strings.

@incollection{statphys23_0042, abstract = {We present an extensive Monte Carlo simulation study on the nonequilibrium kinetics of triangular antiferromagnetic Ising model within the ground state ensemble which consists of sectors, each of which is characterized by a unique value of the string density $p$ through a dimer covering method. In our pevious work(PRE 68, 066127(2003)), we considered the nonequilibrium relaxation with dominant sector $p=2/3$ which is the highest entropic state within ground manifold. Here we extended the nonequilibirum kinetics within the minor sectors with $p<2/3$. As a results of the simulations, we observed emergence of a critical relaxation region which grows as $p$ deviated from $p=2/3$. Spatial anisotropy appears in the equilibrium spatial correlation with the characteristic length scale $\xi_{e,V}(p)$ diverging with vanishing string density as $\xi_{e,V}(p) \sim p^{-2}$ along the vertical direction, while along the horizontal direction the spatial length scale diverges as $\xi_{e,H}(p) \sim p^{-1}$. Analytic forms for the anisotropic equilibrium correlation functions are give. We also find that the spin autocorrelation function $A(t)$ shows a simple scaling behaviour $A(t)=A(t/\tau_A(p))$, where the time scale $\tau_A(p)$ shows a power-law divergence with vanishing p as $\tau_A(p)\sim p^{-\phi}$ with $\phi \simeq 4$. These features can be understood in terms of random walk nature of the fluctuation of the strings within the typical separation between neighbouring strings.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Kim, E. and Lee, S.J. and Kim, B.}, biburl = {https://www.bibsonomy.org/bibtex/2aa91d7bbf5be97035cf40cba647bad84/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {5d07b8955d841a5344b46756b911ff35}, intrahash = {aa91d7bbf5be97035cf40cba647bad84}, keywords = {antiferro-ising frustrated model nonequilibrium relaxation statphys23 system topic-3 triangular}, month = {9-13 July}, timestamp = {2007-06-20T10:16:10.000+0200}, title = {Nonequilibrium relaxation with the ground-state manifold in the antiferromagnetic Ising model on a triangular lattice}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=42}, year = 2007 }