Elektrik - Elektronik Mühendisliği Bölümü Koleksiyonu
Permanent URI for this collectionhttps://gcris.khas.edu.tr/handle/20.500.12469/47
Browse
Browsing Elektrik - Elektronik Mühendisliği Bölümü Koleksiyonu by Author "Atalay, Bora"
Now showing 1 - 2 of 2
- Results Per Page
- Sort Options
Article Citation Count: 13Lower lower-critical spin-glass dimension from quenched mixed-spatial-dimensional spin glasses(Amer Physical Soc., 2018) Atalay, Bora; Berker, A. NihatBy quenched-randomly mixing local units of different spatial dimensionalities we have studied Ising spin-glass systems on hierarchical lattices continuously in dimensionalities 1 <= d <= 3. The global phase diagram in temperature antiferromagnetic bond concentration and spatial dimensionality is calculated. We find that as dimension is lowered the spin-glass phase disappears to zero temperature at the lower-critical dimension d(c) = 2.431. Our system being a physically realizable system this sets an upper limit to the lower-critical dimension in general for the Ising spin-glass phase. As dimension is lowered towards d(c) the spin-glass critical temperature continuously goes to zero but the spin-glass chaos fully subsists to the brink of the disappearance of the spin-glass phase. The Lyapunov exponent measuring the strength of chaos is thus largely unaffected by the approach to d and shows a discontinuity to zero at d(c.)Article Citation Count: 2Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering(Amer Physical Soc., 2018) Atalay, Bora; Berker, A. NihatDiscrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric ferromagnetic or antiferromagnetic including off-diagonal disorder are studied for the number of states q = 34 in d dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d > 1 and all nonmfimte temperatures the system eventually renormalizes to a random single state thus signaling q x q degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus a temperature range of short-range disorder in the presence of long-range order is identified as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures behaves similarly for ferromagnetic and antiferromagnetic interactions and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension 1 + epsilon the system is as expected disordered at all temperatures for d = 1.