Lower and upper bounds on the critical temperature for anisotropic three-dimensional Ising model

Yurishchev, M. A.

doi:10.1134/1.1777631

Cited by 7 publications

(2 citation statements)

References 37 publications

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“…The upper bound was found by an analysis of the asymptotic properties of self-avoiding random walks on the lattice under consideration. More recently, Yurishchev [7] derived upper and lower bounds on the critical temperature by using the transfer-matrix technique and an extended phenomenological renormalization group theory approach [8,9]. Yurishchev showed that for a relatively small anisotropy ( 510 À3 ) the accuracy of equation (1) is rather low.…”

Section: Introductionmentioning

confidence: 99%

The anisotropic 3D Ising model

2007

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An expression for the free energy of an (001) oriented domain wall of the anisotropic 3D Ising model is derived. The order-disorder transition takes place when the domain wall free energy vanishes. In the anisotropic limit, where two of the three exchange energies (e.g. J x and J y ) are small compared to the third exchange energy (J z ), the following asymptotically exact equation for the critical temperature is derived, sinh(2J z /k B T c )sinh(2(J x þ J y )/k B T c )) ¼ 1. This expression is in perfect agreement with a mathematically rigorous result Griffiths and Fisher (Phys. Rev. 162, 475 (1967)) using an approach that relies on a refinement of the Peierls argument. The constant that was left undetermined in the Weng et al. result is estimated to vary from $0.84 at ((H x þ H y )/H z ) ¼ 10 À2 to $0.76 at ((H x þ H y )/H z ) ¼ 10 À20 .

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Section: Introductionmentioning

confidence: 99%

The anisotropic 3D Ising model

2007

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“…We then note that, if we use the above estimates of J 2 9.3 meV and J 1 = J 3 −1.17 meV, the 2D Ising critical temperature with S = 3/2 of each layer n and n + 1/2 is about 0.4 (S + 1/2) 2 J 2 173 K [47]. That corresponds to I 6.6 meV [50]. The 3D Ising critical temperature T c T N depends on the anisotropy ratio I ⊥ /I [50], being at most 345 K for I ⊥ /I 1 1, and reaching the observed T N 290 [12] at I ⊥ /I 1 0.75, which we find not unrealistic.…”

Section: Effective Heisenberg Modelmentioning

confidence: 78%

Order from disorder phenomena in BaCoS$_2$

Lenz¹,

Fabrizio²,

Casula³

2023

Preprint

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At TN305 K the layered insulator BaCoS2 transitions to a columnar antiferromagnet that signals non-negligible magnetic frustration despite the relatively high TN , all the more surprising given its quasi two-dimensional structure. Here, we show, by combining ab initio and model calculations, that the magnetic transition is an order-from-disorder phenomenon, which not only drives the columnar C4 → C2 symmetry breaking, but also, and more importantly, the inter-layer coherence responsible for the finite Néel transition temperature. This uncommon ordering mechanism, actively contributed by orbital degrees of freedom, hints at an abundance of low energy excitations below and, especially, above TN , not in disagreement with experimental evidences, and might as well emerge in other layered correlated compounds showing frustrated magnetism at low temperature.

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