Numerical evidence that the number of pure states in the spin glass phase is infinite near the ferromagnetic phase boundary for the three dimensional (3D) ± J Ising model and 3D gauge glass models is presented. It is consistent with the mean field theory which suggests the multivalley structure of the spin glass phase. We will show that the onset of the ferromagnetic long-range order and that of the ferromagnetic spontaneous symmetry breaking do not coincide with each other, and this phenomenon characterizes the structure of the phase space.Numerical evidence that the number of pure states in the spin glass phase is infinite near the ferromagnetic phase boundary for the three dimensional (3D) ± J Ising model and 3D gauge glass models is presented. It is consistent with the mean field theory which suggests the multivalley structure of the spin glass phase. We will show that the onset of the ferromagnetic long-range order and that of the ferromagnetic spontaneous symmetry breaking do not coincide with each other, and this phenomenon characterizes the structure of the phase space.

Journal of the Physical Society of JapanDec 15, 200113 citations

Local phase-space structure and low-temperature dynamics of short-range Ising spin glasses

Paolo Sibani, Peter Schriver

We study the phase-space geometry and the low-temperature relaxation of short-range Gaussian Ising spin-glasses, by finding all the configurations and their interconnection within a ``pocket'' of states surrounding a low-lying energy minimum. Thermalization within the pocket is modeled by a master equation, which is solved numerically, yielding the time-dependent propagator. The findings show that the relaxation proceeds by a series of local equilibrations in nested ``valleys,'' and support the dynamical predictions of hierarchical relaxation models.We study the phase-space geometry and the low-temperature relaxation of short-range Gaussian Ising spin-glasses, by finding all the configurations and their interconnection within a ``pocket'' of states surrounding a low-lying energy minimum. Thermalization within the pocket is modeled by a master equation, which is solved numerically, yielding the time-dependent propagator. The findings show that the relaxation proceeds by a series of local equilibrations in nested ``valleys,'' and support the dynamical predictions of hierarchical relaxation models.

Physical review. B, Condensed matterMar 1, 199450 citations

Phase Transition of Three-Dimensional Site-Random Ising Model with Short-Range Interactions

Takayuki Shirakura, Fumitaka Matsubara

We study a short-range site-random Ising model in three dimensions (3D) using a Monte Carlo (MC) method and find a phase transition to a spin glass (SG) phase at a very high temperature ( T c ≃2.83 J). Values of the critical exponents estimated from a finite-size scaling analysis are different from those in both the 3D $\mp J$ Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.We study a short-range site-random Ising model in three dimensions (3D) using a Monte Carlo (MC) method and find a phase transition to a spin glass (SG) phase at a very high temperature ( T c ≃2.83 J). Values of the critical exponents estimated from a finite-size scaling analysis are different from those in both the 3D$\mp J$ Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.

Journal of the Physical Society of JapanSep 15, 19939 citations

\mp J

Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.