Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of Spin-Glass Systems

Abstract

The spin-1/2 quantum Heisenberg spin-glass system is studied in all spatial dimensions d by renormalization-group theory. Strongly asymmetric phase diagrams in temperature and antiferromagnetic bond probability p are obtained in dimensions d ≥ 3. The asymmetry at high temperatures approaching the pure ferromagnetic and antiferromagnetic systems disappears as d is increased. However, the asymmetry at low but finite temperatures remains in all dimensions, with the antiferromagnetic phase receding to the ferromagnetic phase. A finite-temperature second-order phase boundary directly between the ferromagnetic and antiferromagnetic phases occurs in d ≥ 6, resulting in a new multicritical point at its meeting with the boundaries to the paramagnetic phase. In d = 3, 4, 5, a paramagnetic phase reaching zero temperature intervenes asymmetrically between the ferromagnetic and reentrant antiferromagnetic phases. There is no spin-glass phase in any dimension.PACS numbers: 75.10. Nr, 64.60.Ak, 05.45.Df, 05.10.Cc A conspicuous finite-temperature effect of quantum mechanics is the critical temperature differentiation between ferromagnetic and antiferromagnetic systems. [1,2,3,4] This is a contrast to classical systems where, e.g., on loose-packed lattices ferromagnetic and antiferromagnetic systems are mapped onto each other and therefore have the same critical temperature. We find that this quantum effect is compounded and even more robust in spin-glass systems, which incorporate the passage from ferromagnetism and antiferromagnetism via quenched disorder.Thus, in the present work, the phase diagrams of the spin-1/2 quantum Heisenberg spin-glass systems are calculated in all dimensions d ≥ 3. In the space of temperature T and concentration p of antiferromagnetic bonds, remarkably asymmetric phase diagrams are obtained, in very strong contrast to the corresponding classical systems. Whereas, in the limit of d → ∞, the differentiation of the critical temperatures of the ferromagnetic and antiferromagnetic pure systems disappears, the T p phase diagrams remain strongly asymmetric at low but finite temperatures, where quantum fluctuations remain dominant independent of dimensionality. A direct second-order phase boundary between ferromagnetic and antiferromagnetic phases, also not seen in isotropic classical systems, is found in d > 5. In lower d, a paramagnetic phase intervenes between the ferromagnetic and antiferromagnetic systems. Our calculation is an approximation for hypercubic lattices and, simultaneously, a lesser approximation for hierarchical lattices [5,6,7,8,9,10,11,12,13,14,15].The spin-1/2 quantum Heisenberg spin-glass systems have the Hamiltonian −βH = ij J ij s i · s j ≡ ij −βH(i, j), where ij denotes a sum over pairs of nearest-neighbor sites. J ij is equal to the ferromagnetic value of J > 0 with probability 1 − p and to the antiferromagnetic value of −J < 0 with probability p. We solve this model by extending the Suzuki-Takano rescaling [3,4,16,17,18,19,20,21,22,23,24] to non-uniform systems and to length-re...

Uncovering the secrets of the 2D random-bond Blume–Capel model

“…It was then pointed out that this naturally leads to a higher transition temperature and effectively carries the ordering system to higher non-zero spin densities, the domain of second-order phase transitions. A similar microsegregation phenomenon, of the s i = ±1 states and of the s i = 0 state, has been seen in the low-temperature second-order transition between different ordered phases under quenched randomness [ 13].…”

Phase transitions between different spin-glass phases and between different chaoses in quenched random chiral systems

“…Similar previous studies, on other spin-glass systems, are reported in Refs. [12,13,[40][41][42][43][44][45][46][47]. Figure 1 shows a calculated sequence of phase diagram cross sections for the left-chiral (c = 0) (top row) and quenched random left-and right-chiral (c = 0.5) (bottom row) systems with, in both cases, quenched random ferromagnetic and antiferromagnetic interactions.…”

Chiral Potts spin glass ind=2and 3 dimensions

“…However, as noted before [45], the local summation in position-space technique used here has been qualitatively, near-quantitatively, and predictively successful in a large variety of problems, such as arbitrary spin-s Ising models [46], global BlumeEmery-Griffiths model [47], first-and second-order Potts transitions [48,49], antiferromagnetic Potts critical phases [50,51], ordering [6] and superfluidity [52] on surfaces, multiply reentrant liquid crystal phases [53,54], chaotic spin glasses [55], random-field [56,57] and random-temperature [58,59] magnets, including the remarkably small d = 3 magnetization critical exponent β of the random-field Ising model, and high-temperature superconductors [60]. Thus, this renormalization-group approximation continues to be widely used [61][62][63][64][65][66][67][68][69][70][71][72][73][74].…”

“…We effect this procedure numerically, by representing each probability distribution by histograms, as in previous studies [62,[64][65][66]68,69,72,74]. The probability distributions of two interactions P 0 (J + ,J − ), P + (J 0 ,J − ), and P − (J + ,J − ) are represented via bivariate histograms with two-dimensional vectors (J + ,J − ) for P 0 , etc.…”

“…Similar previous studies, on other spin-glass systems, are in Refs. [61][62][63][64][65][66][67][68][69][70][71][72][73][74].…”