%0 Book Section %1 statphys23_0353 %A Melchert, O. %A Hartmann, A.K. %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 glasses minimum paths spin statphys23 topic-9 weight %T Fractal dimension of domain walls in two-dimensional Ising spin glasses %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=353 %X We study domain walls (DWs) in 2d Ising spin glasses, see Figure 1, in terms of a minimum-weight path problem. Using this approach, large systems can be treated exactly. Our focus is on the fractal dimension $d_f$ of domain walls, which describes via $\rangle\!\sim\!L^d_f$ the growth of the average domain-wall length with systems size $L$. Exploring systems up to $L\!=\!320$ we yield $d_f\!=\!1.274(1)$ for the case of Gaussian disorder, in support of previous findings. Together with the stiffness exponent $= 0.287(4)$ $1$, that describes the scaling of the DW energy with system size according to $\Delta E L^-þeta$, our result is consistent with the recently proposed scaling relation $d_f-1 = 3/4(3+þeta)$, derived from the context of stochastic Loewner evolution processes using conformal field theory $2$. For the case of bimodal disorder, where many equivalent domain walls exist due to the degeneracy of this model, we obtain a true lower bound $d_f\!=\!1.095(1)$ and an estimate $d_f\!=\!1.395(1)$ for the upper bound. These exponents describe the scaling of the DWs with minimal length and maximal length, respectively. This is in contrast to recent studies, that aimed to capture the properties of typical DWs $3$, resulting in $d_f=1.30(1)$. Furthermore, we study the distributions of the domain-wall lengths. Their scaling with system size can be described solely by the exponent $d_f$, i.e.\ the distributions are monofractal. Finally, we investigate the growth of the domain-wall roughness with system size and find a linear behavior.\\ 1) A.K.~Hartmann and A.P.~Young, Phys. Rev. B 64 (2001) 180404\\ 2) C.~Amoruso et. al., Phys. Rev. Lett. 97 (2006) 267202\\ 3) F.~Romá et. al., Phys. Rev. B 75 (2007) 020402(R)

@incollection{statphys23_0353, abstract = {We study domain walls (DWs) in 2d Ising spin glasses, see Figure 1, in terms of a minimum-weight path problem. Using this approach, large systems can be treated exactly. Our focus is on the fractal dimension $d_f$ of domain walls, which describes via $\langle \ell \rangle\!\sim\!L^{d_f}$ the growth of the average domain-wall length with systems size $L$. Exploring systems up to $L\!=\!320$ we yield $d_f\!=\!1.274(1)$ for the case of Gaussian disorder, in support of previous findings. Together with the stiffness exponent $\theta = 0.287(4)$ \mbox{$[1]$}, that describes the scaling of the DW energy with system size according to $\Delta E \sim L^{-\theta}$, our result is consistent with the recently proposed scaling relation $d_f-1 = 3/[4(3+\theta)]$, derived from the context of stochastic Loewner evolution processes using conformal field theory \mbox{$[2]$}. For the case of bimodal disorder, where many equivalent domain walls exist due to the degeneracy of this model, we obtain a true lower bound $d_f\!=\!1.095(1)$ and an estimate $d_f\!=\!1.395(1)$ for the upper bound. These exponents describe the scaling of the DWs with minimal length and maximal length, respectively. This is in contrast to recent studies, that aimed to capture the properties of typical DWs \mbox{$[3]$}, resulting in $d_f=1.30(1)$. Furthermore, we study the distributions of the domain-wall lengths. Their scaling with system size can be described solely by the exponent $d_f$, i.e.\ the distributions are monofractal. Finally, we investigate the growth of the domain-wall roughness with system size and find a linear behavior.\\ 1) A.K.~Hartmann and A.P.~Young, Phys. Rev. B 64 (2001) 180404\\ 2) C.~Amoruso \emph{et. al.}, Phys. Rev. Lett. 97 (2006) 267202\\ 3) F.~Rom\'a \emph{et. al.}, Phys. Rev. B 75 (2007) 020402(R)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Melchert, O. and Hartmann, A.K.}, biburl = {https://www.bibsonomy.org/bibtex/24663b15cc10c7471e4fef0a246001427/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {9a9bde05d9beb6943e05718ee9ee0e4b}, intrahash = {4663b15cc10c7471e4fef0a246001427}, keywords = {glasses minimum paths spin statphys23 topic-9 weight}, month = {9-13 July}, timestamp = {2007-06-20T10:16:18.000+0200}, title = {Fractal dimension of domain walls in two-dimensional Ising spin glasses}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=353}, year = 2007 }