Numerical study of the overlap Lee–Yang singularities in the three-dimensional Edwards–Anderson model

Abstract

Abstract.We have characterized numerically, using the Janus computer, the Lee-Yang complex singularities related to the overlap in the 3D Ising spin glass with binary couplings in a wide range of temperatures (both in the critical and in the spin-glass phase). Studying the behavior of the zeros at the critical point, we have obtained an accurate measurement of the anomalous dimension in very good agreement with the values quoted in the literature. In addition, by studying the density of the zeros we have been able to characterize the phase transition and to investigate the EdwardsAnderson order parameter in the spin-glass phase, finding agreement with the values obtained using more conventional techniques.

Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks

“…This tendency differs from the one observed above for the zeros in complex t and τ planes (see Fig. 3) and is explained by the form of the scaling variable (25), which incorporates now both the temperature and the system size dependencies.…”

“…It has been suggested [5] that at the critical point the partition function zeros scale as a fraction of their total number j/N for large values of the index j . Moreover, many models give scaling in the ratio (j − C)/N in which C = 1/2 is an empirical fitting factor [24,25]. Recently, a more comprehensive form for the scaling of the Lee-Yang zeros in the critical region was suggested [26].…”

Scaling behavior of the Heisenberg model in three dimensions

“…[13], it was suggested that the partition function zeros could scale, in the critical region, as a fraction of the total number of zeros, i.e., as a function of j/L d , for large values of the index j. In fact many models give scaling in the ratio (j − ǫ)/L d in which ǫ = 1/2 [14,15]. If such a functional form is widespread for Lee-Yang zeros, it suggests that Eq.…”