Absence of an Equilibrium Ferromagnetic Spin-Glass Phase in Three Dimensions

Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3D spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up until the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.

Figure 1

Left: Phase diagram in a mean field model [$\rho$ is the excess concentration of ferromagnetic bonds cf. Eq. (1)]. A mixed (M) phase, with both ferromagnetic (F) ordering and replica symmetry breaking (RSB), is present. At larger temperature the system is paramagnetic (P). Right: The role of the coordination on the presence of such a mixed phase in the mean field picture at temperature $T=0$ (artist’s view).

Figure 2

Scaling plot of $m$ as a function of $\rho$ in the first neighbor model; ${\rho }_{\mathrm{F}}=0.385$, $\nu =0.9$, and $\beta =0.3$. The inset shows the Binder cumulant of $m_J$.

Figure 3

Scaling plot of the mean value of $m$ as a function of $\rho$ in the second neighbor model; ${\rho }_{\mathrm{F}}=0.236$, $\nu =0.9$, and $\beta =0.3$. The inset shows the Binder cumulant of $m_J$.

Figure 4

Fraction of spongelike excitations versus $\rho$ in the FNM. (The inset shows the data for the SNM.) ${\rho }_{\mathrm{R}\mathrm{S}\mathrm{B}}^{\mathrm{F}\mathrm{N}\mathrm{M}}=0.380(5)$ [${\rho }_{\mathrm{R}\mathrm{S}\mathrm{B}}^{\mathrm{S}\mathrm{N}\mathrm{M}}=0.235(5)$].

Figure 5

Fraction of spongy interfaces versus $\rho$ in the FNM. (The inset shows the data for the SNM.) The crossing points drift to the left, suggesting ${\rho }_{\mathrm{D}\mathrm{W}}\approx {\rho }_{\mathrm{R}\mathrm{S}\mathrm{B}}$.