Ordering of the Heisenberg spin glass in four dimensions

Kawamura, Hikaru; Nishikawa, Sayaka

doi:10.1103/physrevb.85.134439

Cited by 4 publications

(7 citation statements)

References 36 publications

(73 reference statements)

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“…(Such an increase of T dip (L) was indeed observed in a recent simulation of the 4D Heisenberg SG 87 .) The behavior originates from the fact that both the dip and the crossing temperatures of g CG should converge to a common value, T CG , each with an exponent 1/ν and θ(> 1/ν), while the crossing temperature always lies above the dip one.…”

Section: Monte Carlo Resultssupporting

confidence: 75%

Monte Carlo simulations of the three-dimensionalXYspin glass focusing on chiral and spin order

Obuchi¹,

Kawamura²

2013

Phys. Rev. B

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The ordering of the three-dimensional isotropic XY spin glass with the nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. To investigate the ordering of the spin and the chirality, we compute several independent physical quantities including the glass order parameter, the Binder parameter, the correlation-length ratio, the overlap distribution and the non-self-averageness parameter, etc, for both the spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of the spin-chirality decoupling, i.e., the CG and the SG order occurring at two separated temperatures, 0 < TSG < TCG, is obtained from the glass order parameter, which is fully corroborated by the Binder parameter. By contrast, the CG correlation-length ratio yields a rather pathological and inconsistent result in the range of sizes we studied, which may originate from the finite-size effect associated with a significant short-length drop-off of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents νCG = 1.36 +0.15 −0.37 and ηCG = 0.26 +0.29 −0.26 , and the SG exponents νSG = 1.22 +0.26 −0.06 and ηSG = −0.54 +0.24 −0.52 . The obtained exponents are close to those of the Heisenberg SG, but are largely different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replicasymmetry breaking (1RSB), consistently with the previous reports. Such a 1RSB feature is again in common with that of the Heisenberg SG, but is different from the Ising one, which may be the cause of the difference in the CG critical properties from the Ising SG ones despite of a common Z2 symmetry.

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Section: Monte Carlo Resultssupporting

confidence: 75%

Monte Carlo simulations of the three-dimensionalXYspin glass focusing on chiral and spin order

Obuchi¹,

Kawamura²

2013

Phys. Rev. B

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“…While several works [10,11] reported the existence of Heisenberg SG in 3D. Recent study by Kawamura and Nishikawa [3] reported that only a chiral glass exists and no spin glass phase found. These various results indicate that more elaborations on the mechanism of the emergence of SG phenomena are required.…”

Section: Introductionmentioning

confidence: 98%

“…The study of spin glasses has been an active research field for almost four decades [1][2][3][4]. It is a random magnetic system which is mainly characterized by a frozen random spins configuration at low temperature.…”

Section: Introductionmentioning

confidence: 99%

Search for the Heisenberg spin glass on rewired square lattices with antiferromagnetic interaction

Surungan¹,

Bj²,

Tahir³

2016

AIP Conference Proceedings

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Abstract. Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect, and aging phenomena. There are two main ingredients considered to be pivotal for the existence of SG behavior, namely, frustration and randomness. For the canonical SG system, frustration is led by the presence of competing interaction between ferromagnetic (FM) and antiferromagnetic (AF) couplings. Previously, Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)], reported the SG properties of the AF Ising spins on scale free network (SFN). It is a new type of SG, different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely caused by the topological factor and its randomness is related to the irregular connectvity. Recently, Surungan et. al. [Journal of Physics: Conference Series, 640, 012001 (2015)] reported SG bahavior of AF Heisenberg model on SFN. We further investigate this type of system by studying an AF Heisenberg model on rewired square lattices. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.

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“…Early numerical study by Coluzzi observed SG phase transition on 4D Heisenberg model. Kawamura and Nishikawa pointed out the absence of Heisenberg SG phase on Ddimensional space, for D ≤ 3 [5]. These works suggested that the lower critical dimension d l might be a fractional number, 3 < d l < 4.…”

Section: Introductionmentioning

confidence: 98%

“…Spin glass (SG) is one of the most complex systems in condensed matter physics and has been intensively studied in the last four decades [1][2][3][4][5][6]. It is a randomly frustrated magnetic system with frozen disordered spin orientation at low temperatures.…”

Section: Introductionmentioning

confidence: 99%

Spin glass behavior of the antiferromagnetic Heisenberg model on scale free network

Surungan

Zen

Williams

2015

J. Phys.: Conf. Ser.

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Randomness and frustration are considered to be the key ingredients for the existence of spin glass (SG) phase. In a canonical system, these ingredients are realized by the random mixture of ferromagnetic (FM) and antiferromagnetic (AF) couplings. The study by Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)] who observed the presence of SG phase on the AF Ising model on scale free network (SFN) is stimulating. It is a new type of SG system where randomness and frustration are not caused by the presence of FM and AF couplings. To further elaborate this type of system, here we study Heisenberg model on AF SFN and search for the SG phase. The canonical SG Heisenberg model is not observed in d-dimensional regular lattices for (d ≤ 3). We can make an analogy for the connectivity density (m) of SFN with the dimensionality of the regular lattice. It should be plausible to find the critical value of m for the existence of SG behaviour, analogous to the lower critical dimension (d l ) for the canonical SG systems. Here we study system with m = 2, 3, 4 and 5. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter. We observed SG phase for each value of m and estimated its corersponding critical temperature.

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Ordering of the Heisenberg spin glass in four dimensions

Cited by 4 publications

References 36 publications

Monte Carlo simulations of the three-dimensionalXYspin glass focusing on chiral and spin order

Monte Carlo simulations of the three-dimensionalXYspin glass focusing on chiral and spin order

Search for the Heisenberg spin glass on rewired square lattices with antiferromagnetic interaction

Spin glass behavior of the antiferromagnetic Heisenberg model on scale free network

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