Quasi-long-range order in random-anisotropy Heisenberg models

Fisch, Ronald

doi:10.1103/physrevb.58.5684

Cited by 31 publications

(33 citation statements)

References 47 publications

(53 reference statements)

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“…17 In three dimensions, instead, the phase diagram has been controversial for a long time. While for small values of D numerical simulations 5,[18][19][20][21][22] confirmed the existence of a finitetemperature transition ͑though QLRO was never observed͒, in the SRAM even the existence of the transition was in doubt. 21 In Ref.…”

Section: Introductionmentioning

confidence: 95%

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Liers¹,

Lukic²,

Marinari³

et al. 2007

Phys. Rev. B

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We consider the random-anisotropy model on the square and on the cubic lattice in the strong-anisotropy limit. We compute exact ground-state configurations, and we use them to determine the stiffness exponent at zero temperature; we find theta=-0.275(5) and theta approximate to 0.2, respectively, in two and three dimensions. These results strongly suggest that the low-temperature phase of the model is the same as that of the usual Ising spin-glass model. We also show that no magnetic order occurs in two dimensions, since the expectation value of the magnetization is zero and spatial correlation functions decay exponentially. In three dimensions, our data strongly support the absence of spontaneous magnetization in the infinite-volume limit

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Section: Introductionmentioning

confidence: 95%

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Liers¹,

Lukic²,

Marinari³

et al. 2007

Phys. Rev. B

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“…In the RAN model, Cleaver et al [49] found that the low temperature phase of the RAN model, at least for one value of D, exhibited QLRO, while Chakrabarti [58] asserted that there was a value of D below which LRO was retained. Extensive simulations [65,66] suggest that LRO is lost even at low D in the analogous magnetic models. The Larkin-Imry-Ma theory in the RAN case [49] suggests that the LRO should always be unstable at least with respect to the formation of domains, with short-range order, and this is in general what has been found in a number of studies on the SSS model [22,[61][62][63].…”

Section: Introductionmentioning

confidence: 99%

Computational studies of history dependence in nematic liquid crystals in random environments

et al. 2014

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Glassy liquid crystalline systems are expected to show significant history-dependent effects. Two model glassy systems are the RAN and SSS lattice models. The RAN model is a Lebwohl-Lasher lattice model with locally coupled nematic spins, together with uncorrelated random anisotropy fields at each site, while the SSS model has a finite concentration of impurity spins frozen in random directions. Here Brownian simulation is used to study the effect of different sample histories in the low temperature regime in a three dimensional (d = 3) model intermediate between SSS and RAN, in which a finite concentration p < pc (pc the percolation threshold) of frozen spins interacts with neighboring nematic spins with coupling W . Simulations were performed at temperature T ∼ TNI /2 (TNI the bulk nematic-isotropic transition temperature) for temperature-quenched and field-quenched histories (TQH and FQH respectively), as well as for temperature-annealed histories (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. Using long-time averages for equilibrated systems, we calculate orientational order parameters and two-point correlation functions. Finite size-scaling was used to determine the range of the orientational ordering, as a function of coupling strength W, p and sample history. Sample history plays a significant role; for given concentration p, as disorder strength W is increased, TQH systems sustain quasi-long-range (QLRO) and short-range-order (SRO). The data are also consistent with a long-range order (LRO) phase at very low disorder strength. By contrast, for FQH, only LRO and QLRO occur within the range of parameters investigated. The crossover between regimes depends on history, but in general, the FQH phase is more ordered than than the AH phase, which is more ordered than the TQH phase. We detect also in the QLRO phase a domain-type structural pattern, consistent with ideas introduced by Giamarchi and Doussal [Phys. Rev. B 52, 1242Rev. B 52, (1995] on superconducting flux lattices. In phases in which short-range exponential order occurs, the orientational correlation length in the weak-disorder limit obeys Larkin-Imry-Ma scaling ξ ∼ D −2/(4−d) .

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“…While an Imry-Ma-type argument 7 of model ͑1͒ leads to a conclusion that any nonzero anisotropy D destroys long-range magnetic order in three dimensions, it is predicted by field theoretical analysis 2,10,11 that the model realizes QLRO at lowtemperature and weak-anisotropy region. Numerical studies of model ͑1͒ have been restricted to approximate discretized models or small sizes, [12][13][14] and the QLRO phase was numerically confirmed in Ref. 14.…”

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confidence: 99%

Frozen quasi-long-range order in the random anisotropy Heisenberg magnet

Itakura¹

2003

Phys. Rev. B

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Extensive Monte Carlo simulations are used to investigate the low-temperature properties of the random anisotropy Heisenberg model, which describes the magnetic behavior of amorphous rare-earth-transition metal alloy. We show that the low-temperature phase in weak-anisotropy region is characterized by a frozen-in power-law spin-spin correlation. Numerical observation of the power-law exponent indicates nonuniversal behavior.Power-law correlation, or quasi-long-range order ͑QLRO͒, usually emerges just at the critical temperature of phase transition. The notable exception is the Kosterlitz-Thouless phase of two-dimensional XY model, in which power-law correlation persists down to zero temperature. 1 Recently, it has been found that the low-temperature QLRO phase is quite common in disordered three-dimensional systems, 2 such as the so-called ''Bragg-glass phase'' of impure superconductors, 3,4 nematic phase of liquid crystal in a porous media, 5,6 and amorphous rare-earth-transition metal alloy. 8 These systems are described either by random-field or random anisotropy spin models. Harris, Plischke, and Zuckermann first used the following random anisotropy model to study amorphous metal magnet: 9HϭϪJ ͚ ͗i j͘ S ជ i •S ជ j ϪD ͚ i RAPID COMMUNICATIONS PHYSICAL REVIEW B 68, 100405͑R͒ ͑2003͒

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Quasi-long-range order in random-anisotropy Heisenberg models

Cited by 31 publications

References 47 publications

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Computational studies of history dependence in nematic liquid crystals in random environments

Frozen quasi-long-range order in the random anisotropy Heisenberg magnet

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