Toward a final theory of critical exponents in terms of dimensionality d plus universality class n

March, N. H.

doi:10.1016/j.physleta.2014.11.043

Cited by 6 publications

(6 citation statements)

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“…[68,69] obey the standard scaling relations, as they should, a logarithmic term in the specific heat would contradict the scaling relations for logarithmic corrections [73]. The recent claims of [69] and related papers [71] were criticised in Refs. [72].…”

Section: More On Exact Solutionsmentioning

confidence: 99%

The fate of Ernst Ising and the fate of his model

Ising¹,

Folk²,

Kenna³

et al. 2017

J. Phys. Stud.

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On this, the occasion of the 20th anniversary of the "Ising Lectures" in Lviv (Ukraine), we give some personal reflections about the famous model that was suggested by Wilhelm Lenz for ferromagnetism in 1920 and solved in one dimension by his PhD student, Ernst Ising, in 1924. That work of Lenz and Ising marked the start of a scientific direction that, over nearly 100 years, delivered extraordinary successes in explaining collective behaviour in a vast variety of systems, both within and beyond the natural sciences. The broadness of the appeal of the Ising model is reflected in the variety of talks presented at the Ising lectures (http://www.icmp.lviv.ua/ising/) over the past two decades but requires that we restrict this report to a small selection of topics. The paper starts with some personal memoirs of Thomas Ising (Ernst's son). We then discuss the history of the model, exact solutions, experimental realisations, and its extension to other fields.

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Section: More On Exact Solutionsmentioning

confidence: 99%

The fate of Ernst Ising and the fate of his model

Ising¹,

Folk²,

Kenna³

et al. 2017

J. Phys. Stud.

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“…Furthermore, Zhang's results agree with some experimental results, which are carefully performed with high accuracy (see in [31], for instance). After its publication [3], Zhang's conjectured solution has received supports from several groups, for instance, March and his co-workers [32][33][34][35][36], Ławrynowicz and some mathematicians [6,7,37,38], Kaupuzs and his colleagues [30,39,40], and others [41][42][43][44][45][46][47][48][49][50][51][52][53]. In [8], Zhang-Suzuki-March rigorously proved four Theorems, which verifies the correctness of the Zhang's conjectured solution [3].…”

Section: Introductionmentioning

confidence: 99%

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

Сузукі

Zhang

2021

Mathematics

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A method of the Riemann–Hilbert problem is applied for Zhang’s conjecture 1 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in the zero external field and the solution to the Zhang’s conjecture 1 is constructed by use of the monoidal transform. At first, the knot structure of the ferromagnetic 3D Ising model in the zero external field is determined and the non-local behavior of the ferromagnetic 3D Ising model can be described by the non-trivial knot structure. A representation from the knot space to the Clifford algebra of exponential type is constructed, and the partition function of the ferromagnetic 3D Ising model in the zero external field can be obtained by this representation (Theorem I). After a realization of the knots on a Riemann surface of hyperelliptic type, the monodromy representation is realized from the representation. The Riemann–Hilbert problem is formulated and the solution is obtained (Theorem II). Finally, the monoidal transformation is introduced for the solution and the trivialization of the representation is constructed (Theorem III). By this, we can obtain the desired solution to the Zhang’s conjecture 1 (Main Theorem). The present work not only proves the Zhang’s conjecture 1, but also shows that the 3D Ising model is a good platform for studying in deep the mathematical structure of a physical many-body interacting spin system and the connections between algebra, topology, and geometry.

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“…However, we were saddened when only a few weeks ago some more recent papers [6,7,8,9] came to our attention. March still advocates a theory of the critical exponents based on α = 0 and γ = 5/4 for the threedimensional Ising model.…”

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confidence: 99%

“…from which we calculated ν = 0.62998(3), η = 0.036302 (12), α = 0.11007 (7), β = 0.326423 (18), γ = 1.23708(5), δ = 4.78982 (7),…”

mentioning

confidence: 99%

“…In his articles in Physics Letters [6,7] March does not cite the comments on Zhang's work but he refers to them in [8], where he gives the impression that someone only has to prove two conjectures by Zhang, even though these have been disproved already. March also suggests in [6,7] that Zhang's critical exponents α = 0 and γ = 5/4 agree within experimental accuracy with all existing experiments and theory. This is falsified in many works, as discussed above.…”

mentioning

confidence: 99%

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