Scaling properties of S>1/2 Ising spin glasses

The spin-1 Ising spin glass: a renormalization-group approach

“…One sees no low-temperature re-entrance in the SG phase; this result is in better agreement with the mean-field phase diagram of da Costa et al [17] than with the one of Mottishaw and Sherrington [16]. Except for the phases P 0 and P 1 , the phase diagram shown in figure 2 is qualitatively analogous to the one by Li et al [21] (cf figure 5 of [21]), which used a different RG approach for the spin-1 Ising spin glass. In figure 3 slices of the phase diagram for typical choices of the average value of the initial distribution of crystal fields; it should be mentioned that such planes are noninvariant under the present RG transformation.…”

“…(iii) The spin-glass lower critical dimension does not seem to be significantly affected by the inclusion of the state S i = 0. The present work is in agreement with a previous RG analysis [21], leading to 2 d l 3 for the spin-1 Ising spin glass, in analogy to what happens for the corresponding spin- 1 2 model [6][7][8][9][10][11][12]. Although the spin-glass phase may occur at lower temperatures, as compared to the one of the spin- 1 2 case, due to a weakening of the long-range spin-glass correlations among the spins at states S i = ±1, the lattice dimension seems to be determinant for the occurrence of spin-glass order at finite temperatures.…”

“…However, very little is known about the nearest-neighbour-interaction spin-1 Ising spin glass. Li et al [21] have considered this system, for symmetric coupling probability distributions, through zero-temperature domainwall techniques, in two dimensions, and for both two-and three-dimensional cases, within a MKRG approach. The MKRG phase diagram, in the three-dimensional case, for the system in the presence of a crystal field, yields a critical line with no reentrance, in better agreement with the mean-field predictions of da Costa et al [17], as compared with those of Mottishaw and Sherrington [16].…”

“…The model is studied through the MKRG approach, which is exact for pure systems on such lattices [22][23][24] and expected to yield good approximations for random systems. The purpose of the present work is to show new results for the spin-1 Ising spin glass; several phase diagrams, not considered in [21], are presented, for lattices with fractal dimensions d = 2, 3 and 4. In particular, two phases associated with distinct zeroeffective-coupling-constant attractors are found; to our knowledge, such phases have never been identified in such a model.…”