Evidence for nonuniversal scaling in dimension-four Ising spin glasses

The critical behavior of the Binder cumulant for Ising spin glasses in dimension four is studied through simulation measurements. Data for the bimodal interaction model are compared with those for the Laplacian interaction model. Special attention is paid to scaling corrections. The limiting infinite size value at criticality for this dimensionless variable is a parameter characteristic of a universality class. This critical limit is estimated to be equal to 0.523(3) in the bimodal model and to 0.473(3) in the Laplacian model.

Figure 1

Scaling plots for the Binder cumulant of $4\mathrm{D}$ ISGs, $g(\beta ,2L)/g(\beta ,L)$ vs $g(\beta ,L)$. Red (gray): Laplacian interactions; black: bimodal interactions. Squares, circles, triangles, inverted triangles, and diamonds are for $L=3,4,5,6,7$, respectively.

Figure 2

The Binder cumulant of the $4\mathrm{D}$ bimodal ISG near criticality. Inverse temperatures $\beta =0.510,0.5075,0.505,0.5025,0.500,0.4975$ are shown from top to bottom. Red squares: present data. Black circles: read from Ref. [14]. The two data sets are consistent. The dashed straight line indicates criticality.

Figure 3

The Binder cumulant of the $4\mathrm{D}$ Laplacian ISG near criticality. Inverse temperatures $\beta =0.626,0.624,0.622,0.620,0.618$ are shown from top to bottom. The dashed straight line indicates criticality.

Figure 4

Scaling plot for the bimodal model $W_q(\beta ,L)$ derivative peak location ${\beta }_m$ against the inverse derivative peak height $1/D_m\left(L\right)$.