http://www.bibsonomy.org/burst/user/statphys23/almeida-thoulessBibSonomy BuRST Feed for /user/statphys23/almeida-thouless2008-07-26T21:36:14+02:00http://www.bibsonomy.org/bibtex/261e5c76025e2fff02f105552e1f38851/statphys23statphys232007-06-20T10:16:09+02:00glass edwards-anderson topic-7 statphys23 almeida-thouless method group domain-wall renormalization line spin model <span style="color:#555555;">M. <a href="http://www.bibsonomy.org/author/Sasaki">Sasaki</a> and K. <a href="http://www.bibsonomy.org/author/Hukushima">Hukushima</a> and H. <a href="http://www.bibsonomy.org/author/Yoshino">Yoshino</a> and H. <a href="http://www.bibsonomy.org/author/Takayama">Takayama</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyDomain-Wall Renormalization-Group Study of the Edwards-Anderson Ising Spin Glass in a Magnetic Field2007glass edwards-anderson topic-7 statphys23 almeida-thouless method group domain-wall renormalization line spin model In spite of extensive studies for more than two decades, a basic problem on the field-temperature phase diagram of the short-range Ising spin glass is still controversial. The mean-field picture insists the existence of the spin glass phase in magnetic field. This means that a transition from paramagnetic phase to spin glass phase occurs at a finite temperature if field is smaller than some critical value $H_{\rm c}$. On the other hand, the droplet theory, which is a phenomenological theory for short-range spin glasses, predicts that the spin-glass order is unstable even against an infinitesimal field. It is a long-standing question whether the spin glass phase in field exists in real Ising spin glasses or not. In this work, we study the Edwards-Anderson (EA) short-range Ising spin glass in field $H$ by a numerical domain-wall renormalization-group method [1]. This method enables us to measure effective couplings $J_{\rm eff}$ and effective fields $H_{\rm eff}$ of length scale $L$ within the block spin picture. Because $J_{\rm eff}$ and the free-energy difference $\delta F$ caused by changing the boundary condition from periodic to anti-periodic are related by $J_{\rm eff}=-\delta F/2$ in zero field, we consider that $J_{\rm eff}$ represents the strength of the spin-glass order. Since $J_{\rm eff}$ is either positive or negative, we calculate the standard deviation of sample-to-sample fluctuations of the effective couplings, $\sigma_{\rm J}(L,H)$. The figure shows result of the three-dimensional $\pm J$ EA Ising spin glass. In the inset, $\sigma_{\rm J}$ is plotted as a function of $L$. In the main frames, we test the scaling \begin{equation} \sigma_{\rm J}(L,H) /\ell(H)^{\theta} =\tilde{\sigma}_{\rm J}[L/\ell(H)], \end{equation} predicted by the droplet theory. In this equation, $\ell(H)=H^{\frac{1}{d/2-\theta}}$ is the overlap length, $\theta$ is the stiffness exponent, $d$ is the dimension, and $\tilde\sigma_{\rm J}$ is scaling function. $d$ is fixed to $3$ and $\theta$ is estimated by fitting. Although the value of $\theta$ is a bit higher than previous estimations (around 0.25), the scaling works nicely. We also find that the scaling function $\tilde{\sigma}_{\rm J}(X)$ drops to zero for large $X$. This means that the spin-glass order is destroyed by field beyond the crossover length. Since the crossover length obeys a power law of $H$ which diverges as $H \rightarrow 0$ but remains finite for any non-zero $H$, the scaling implies that the spin-glass phase is absent even in an infinitesimal field.\vspace{2mm} 1) M.Sasaki, K. Hukushima, H. Yoshino and H. Takayama, cond-mat/0702302.