%0 Book Section %1 statphys23_0171 %A Matsuda, Y. %A Nishimori, 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 exact function glass lee-yang matrix partition spin statphys23 topic-9 transfer zeros %T Distribution of Lee-Yang Zeros of the Ising spin glasses %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=171 %X We numerically study the distribution of Lee-Yang zeros of Ising spin glasses on finite lattices. Using the transfer matrix method implemented analytically on the computer by Mathematica, we have computed the zeros up to system sizes $16 16$ and $4 4 6$. Figure 1-a shows an example of the 10 $\times$ 10 lattice at $T=0.5$ on the complex field plane obtained by randomly choosing 17901 samples of bond configurations for the $J$ model. Nearest zeros to the real axis (the Lee-Yang edge) lie on the imaginary axis in the complex field plane. The density of the edge smoothly approaches zero. We call the zeros off the imaginary axis the 'bulk' zeros. We have analyzed the density of this 'edge' and the 'bulk' for various temperatures and system sizes. Figure 1-b shows the location versus system size of the square lattice. We expect that the edge and the bulk touch the real axis , but the non-zero density edge doesn't touch real axis. In fact, there is no spin glass phase in the two-dimensional $J$ model and this analysis is consistent with the phase diagram. The aspect of smooth density zero edge closing in the real axis is similar to zeros of the Griffths phase in diluted ferromagnet. Making use of these results, we discussed spin glass model includes Griffiths singularity. Add to this, we would like to report on the distribution of the three-dimensional model and the Gaussian spin glass model.

@incollection{statphys23_0171, abstract = {We numerically study the distribution of Lee-Yang zeros of Ising spin glasses on finite lattices. Using the transfer matrix method implemented analytically on the computer by Mathematica, we have computed the zeros up to system sizes $16 \times 16$ and $4 \times 4 \times 6$. Figure 1-a shows an example of the 10 $\times$ 10 lattice at $T=0.5$ on the complex field plane obtained by randomly choosing 17901 samples of bond configurations for the $\pm J$ model. Nearest zeros to the real axis (the Lee-Yang edge) lie on the imaginary axis in the complex field plane. The density of the edge smoothly approaches zero. We call the zeros off the imaginary axis the 'bulk' zeros. We have analyzed the density of this 'edge' and the 'bulk' for various temperatures and system sizes. Figure 1-b shows the location versus system size of the square lattice. We expect that the edge and the bulk touch the real axis , but the non-zero density edge doesn't touch real axis. In fact, there is no spin glass phase in the two-dimensional $\pm J$ model and this analysis is consistent with the phase diagram. The aspect of smooth density zero edge closing in the real axis is similar to zeros of the Griffths phase in diluted ferromagnet. Making use of these results, we discussed spin glass model includes Griffiths singularity. Add to this, we would like to report on the distribution of the three-dimensional model and the Gaussian spin glass model.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Matsuda, Y. and Nishimori, H.}, biburl = {https://www.bibsonomy.org/bibtex/2a575b572b39f8d8b0a3c56310264cd5a/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {b7b02a8370d2967b216f288d40ce1770}, intrahash = {a575b572b39f8d8b0a3c56310264cd5a}, keywords = {exact function glass lee-yang matrix partition spin statphys23 topic-9 transfer zeros}, month = {9-13 July}, timestamp = {2007-06-20T10:16:13.000+0200}, title = {Distribution of Lee-Yang Zeros of the Ising spin glasses}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=171}, year = 2007 }