Random-field Ising model on hierarchical lattices: thermodynamics and ground-state critical properties

Low-energy excitations in the three-dimensional random-field Ising model

“…for the ǫ-coupling method (top), the randomexcitation method (middle), and the single-spin flip method (bottom). In all three cases we observe a A ∼ V ds/d behavior (shown as lines) with ds being the fractal dimension, as shown in (6).…”

“…We fitted a power law of the form A = cV ds/d to the data of each method. The resulting fractal dimensions for each method are d s = 2.34(2) single spin flip d s = 2.37(1) random excitations d s = 2.36(1) ǫ-coupling (6) This means the three different types of excitations behave similar within error bars. Compared with the fractal dimensions calculated in [25] (d c s = 2.27 ± 0.02 for clusters and d d s = 2.3 ± 0.04 for domain walls), our fractal dimension of small excitations is compatible with the exponent for domain walls d d s .…”

“…Similar to the more prominent spin glasses (SGs) [2,3,4], there are still many open questions concerning the low-temperature properties of the RFIM. During the last few years, the RFIM and the related diluted antiferromagnet in a field have attracted growing attention [5,6,7,8,9,10,11,12,13,14,15,16], in particular within simulation studies at finite [17,18,19,20,21,22,23], and zero temperature [24,25,26,27,28,29,30,31,32,33,34,35,36].…”

Spin-glass attractor on tridimensional hierarchical lattices in the presence of an external magnetic field

“…, the corresponding RG equations may be written in the general form (see Ref. [32] for the explicit form of these equations for the MK cell of Fig. 1(a)),…”

“…At zero temperature Eqs. (6)-(8) become much simpler (see, e.g., Ref [32]. for the explicit form of these equations for the MK cell of…”