%0 Book Section %1 statphys23_0326 %A Fernandes, H.A. %A Caparica, A.A. %A Silva, R. Da %A Fel\'ıcio, J.R.D. De %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 classical critical exponents finite-size global montecarlo persistence probability scaling simulations statphys23 topic-3 %T Short-time critical dynamics of three-dimensional spin models with continuous symmetry %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=326 %X In this work, we study the dynamic critical behavior of the three-dimensional Heisenberg (HM) and double-exchange (DEM) models through short-time Monte Carlo simulations Fernandes2005,Fernandes2006a,Fernandes2006b. The hamiltonian of the models are given, respectively, by eqnarray* H_HM=-J\sum_i,jS_i\cdot S_j eqnarray* and eqnarray* H_DEM=-J\sum_łangle i,j1+\mathbfS_iS_j eqnarray* where $J>0$ is the ferromagnetic coupling constant, $S_i=(S_i^x,S_i^y,S_i^z)$ is a three-dimensional vector of unit length, located on each site of a simple cubic lattice, and $i,j$ indicates that the sum runs over the pairs of nearest-neighbors of the lattice sites. The dynamic critical exponents $z$, $þeta$, and $þeta_g$, as well as, the static critical exponents $\nu$ and $\beta$ were estimated by following the time evolution of the total magnetization and its moments of higher order. The anomalous dimension of the magnetization $x_0$ was obtained through the scaling relation $x_0=z + \beta/\nu$ which is found in systems out-of-equilibrium. Our estimates for $z$, $\nu$, and $\beta$, for both models, are in good agreement with each other and with values found in the literature. The exponents $þeta$ and $þeta_g$ for the Heisenberg and double-exchange models are in complete agreement with each other, asserting once more the idea which both models belong to the same universality class. To our knowledge, this is the first time that the exponents $þeta$ and $þeta_g$ are calculated for three-dimensional models with continuous spin variables.\\ H.A. Fernandes, J.R. Drugowich de Fel\'ıcio, and A.A. Caparica, Short-time behavior of a classical ferromagnet with double-exchange interaction, Phys. Rev. B. 72, 054434 (2005).\\ H. A. Fernandes and J. R. Drugowich de Fel\'ıcio, Global persistence exponent of the double-exchange model, Phys. Rev. E 73, 57101 (2006).\\ H. A. Fernandes, Roberto da Silva, and J. R. Drugowich de Fel\'ıcio, Short-time critical and coarsening dynamics of the classical three-dimensional Heisenberg model, J. Stat. Mech.: Theor. Exp., P10002 (2006).

@incollection{statphys23_0326, abstract = {In this work, we study the dynamic critical behavior of the three-dimensional Heisenberg (HM) and double-exchange (DEM) models through short-time Monte Carlo simulations \cite{Fernandes2005,Fernandes2006a,Fernandes2006b}. The hamiltonian of the models are given, respectively, by \begin{eqnarray*} \mathcal{H}_{HM}=-J\sum_{\langle i,j\rangle }\mathbf{S}_{i}\cdot \mathbf{S}_{j} \end{eqnarray*} and \begin{eqnarray*} \mathcal{H}_{DEM}=-J\sum_{\langle i,j\rangle }\sqrt{1+\mathbf{S}_{i}\cdot \mathbf{S}_{j}} \end{eqnarray*} where $J>0$ is the ferromagnetic coupling constant, $\textbf{S}_{i}=(S_{i}^{x},S_{i}^{y},S_{i}^{z})$ is a three-dimensional vector of unit length, located on each site of a simple cubic lattice, and $\langle i,j\rangle $ indicates that the sum runs over the pairs of nearest-neighbors of the lattice sites. The dynamic critical exponents $z$, $\theta$, and $\theta_g$, as well as, the static critical exponents $\nu$ and $\beta$ were estimated by following the time evolution of the total magnetization and its moments of higher order. The anomalous dimension of the magnetization $x_0$ was obtained through the scaling relation $x_0=\theta z + \beta/\nu$ which is found in systems out-of-equilibrium. Our estimates for $z$, $\nu$, and $\beta$, for both models, are in good agreement with each other and with values found in the literature. The exponents $\theta$ and $\theta_g$ for the Heisenberg and double-exchange models are in complete agreement with each other, asserting once more the idea which both models belong to the same universality class. To our knowledge, this is the first time that the exponents $\theta$ and $\theta_g$ are calculated for three-dimensional models with continuous spin variables.\\ H.A. Fernandes, J.R. Drugowich de Fel\'{\i}cio, and A.A. Caparica, \textit{Short-time behavior of a classical ferromagnet with double-exchange interaction}, Phys. Rev. B. \textbf{72}, 054434 (2005).\\ H. A. Fernandes and J. R. Drugowich de Fel\'{\i}cio, \textit{Global persistence exponent of the double-exchange model}, Phys. Rev. E \textbf{73}, 57101 (2006).\\ H. A. Fernandes, Roberto da Silva, and J. R. Drugowich de Fel\'{\i}cio, \textit{Short-time critical and coarsening dynamics of the classical three-dimensional Heisenberg model}, J. Stat. Mech.: Theor. Exp., P10002 (2006).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Fernandes, H.A. and Caparica, A.A. and Silva, R. Da and Fel\'{\i}cio, J.R.D. De}, biburl = {https://www.bibsonomy.org/bibtex/26d93867542d99f3185d3e7a460edc357/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {970d6e4abae2a8c8a57320bbcd889f05}, intrahash = {6d93867542d99f3185d3e7a460edc357}, keywords = {classical critical exponents finite-size global montecarlo persistence probability scaling simulations statphys23 topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:17.000+0200}, title = {Short-time critical dynamics of three-dimensional spin models with continuous symmetry}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=326}, year = 2007 }