Nonlocal quartic interactions and universality classes in perovskite manganites

Singh, Rohit; Dutta, Kishore; Nandy, Malay K.

doi:10.1103/physreve.92.012123

Cited by 5 publications

(16 citation statements)

References 47 publications

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“…The exact large-n results just mentioned therefore provide mathematically rigorous evidence against the O(ǫ σ ) series expansions of the critical exponents given in Ref. [1].…”

supporting

confidence: 53%

“…( 27)-(33) of Ref. [1] yields results that are inconsistent with the exact n = ∞ values of these critical exponents, such as ν SDN,∞ = (2 + ǫ σ )/4 + O(ǫ 2 σ ), the only exception being η SDN,∞ = 0. It must be emphasized that the large-n limit is mathematically fully controlled.…”

mentioning

confidence: 92%

“…As a consequence, one arrives at the following mathematically exact statement: The critical exponents of the m > 0 model studied in Ref. [1] have a well-defined ǫ expansion, where the associated series-expansion coefficients of any order in ǫ have exactly the same values as for the standard Φ 4 model with a local Φ 4 (x) interaction.…”

mentioning

confidence: 93%

“…To do this one must study the insertions of all composite operators of the same or lower momentum dimensions (see, e.g., Chapter 10 of [5] or [7]). Upon dropping the irrelevant k-dependent parts of ũ(k), one recovers the standard Φ 4 model with a local Φ 4 (x) term, which therefore represents the universality class of the model (1).…”

mentioning

confidence: 95%

“…The authors of [1] investigated an n-component Φ 4 model in d dimensions with a nonlocal quartic term whose Hamiltonian is given by…”

mentioning

confidence: 99%

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Comment on “Nonlocal quartic interactions and universality classes in perovskite manganites”

Diehl

2016

Phys. Rev. E

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In a recent paper [Phys. Rev. E 92, 012123 (2015)] a modified d-dimensional Φ 4 model was investigated that differs from the standard one in that the Φ 4 term was replaced by a nonlocal one with a potential u(x−x ′ ) that depends on a parameter σ and decays exponentially as |x−x ′ | → ∞ on a scale |m| −1 < ∞. The authors claim the upper critical dimension of this model to be dσ = 4 + 2σ. Performing a one-loop calculation they arrive at expansions in powers of ǫσ = dσ − d for critical exponents such as η and related ones to O(ǫσ) whose O(ǫσ) coefficients depend on σ and the ratio w = m 2 /Λ 2 , where Λ is the uv cutoff. It is shown that these claims are unfounded and based on misjudgments and an ill-conceived renormalization group (RG) calculation. where the potential is specified by its Fourier transformwith a "screening parameter" m 2 > 0. From Eq. (2) one can read off that u(x) falls off exponentially on the scale ξ m = |m| −1 as |x| → ∞ [2]. Hence it is shortranged on the scale of the correlation length ξ(T ) sufficiently close to the critical temperature T c . The reason is that ξ m is temperature-independent or has at most a weak temperature dependence when the interaction is considered as an effective interaction obtained upon coarse graining to a length scale 2π/Λ (> a) on which a continuum approximation is acceptable. Therefore ξ m remains bounded whereas ξ(T ) → ∞ as T → T c , so that lim T →Tc ξ m /ξ → 0 [3]. What matters for the asymptotic critical behavior is just whether or not the interaction is short-ranged on the scale of ξ(T ) as T → T c . This is asymptotically always the case even if ξ m is much larger than the lattice constant a, i.e., if u(x) is long-ranged on the scale of a. Therefore the model must belong to the standard universality class of the d-dimensional n-vector model with short-range interactions represented by the usual Φ 4 model with a local quartic term. The authors' results strongly disagree with this. Performing a one-loop calculation, they conclude that the upper critical dimension of the model is d σ = 4 + 2σ, and they compute some of the critical exponents of the model by an expansion in ǫ σ = d σ − d to first order. The O(ǫ σ ) coefficients of their series expansions depend on σ and m 2 /Λ 2 . If this were true, the critical exponents themselves would have these properties, and hence depend on microscopic details such as m 2 /Λ 2 and be nonuniversal. Obvious serious discrepancies with the modern theory of critical behavior (see, e.g., [4,5] and references therein) would exist. Aside from a gross violation of universality, one would have the following problems: For σ > 0, the asymptotic critical behavior of the model in 4 < d < d σ dimensions would be inconsistent with meanfield theory. Likewise, irrespective of whether σ > 0 or ≤ 0, the critical behavior of the model would differ in d * < d < 4 dimensions from that of the standard Φ 4 model., where d * is the lower critical dimension (= 1 or 2 for n = 1 and n > 1, respectively). However, the authors' claims and their conse...

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“…The exact large-n results just mentioned therefore provide mathematically rigorous evidence against the O(ǫ σ ) series expansions of the critical exponents given in Ref. [1].…”

supporting

confidence: 53%

mentioning

confidence: 92%

mentioning

confidence: 93%

mentioning

confidence: 95%

“…The authors of [1] investigated an n-component Φ 4 model in d dimensions with a nonlocal quartic term whose Hamiltonian is given by…”

mentioning

confidence: 99%

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Comment on “Nonlocal quartic interactions and universality classes in perovskite manganites”

Diehl

2016

Phys. Rev. E

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Magnetoelastic coupling and critical behavior of some strongly correlated magnetic systems

Dutta¹

2022

J. Phys.: Condens. Matter

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The strongly correlated magnetic systems are attracting continuous attention in current condensed matter research due to their very compelling physics and promising technological applications. Being a host to charge, spin, and lattice degrees of freedom, such materials exhibit a variety of phases, and investigation of their physical behavior near such a phase transition bears an immense possibility. This review summarizes the recent progress in elucidating the role of magnetoelastic coupling on the critical behavior of some technologically important class of strongly correlated magnetic systems such as perovskite magnetites, uranium ferromagnetic superconductors, and multiferroic hexagonal manganites. It begins with encapsulation of various experimental findings and then proceeds toward describing how such experiments motivate theories within the Ginzburg-Landau phenomenological picture in order to capture the physics near a magnetic phase transition of such systems. The theoretical results that are obtained by implementing Wilson's renormalization-group to nonlocal Ginzburg-Landau model Hamiltonians are also highlighted. A list of possible experimental realizations of the coupled model Hamiltonians elucidates the importance of spin-lattice coupling near a critical point of strongly correlated magnetic systems.

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Lattice effects and the critical behavior of gadolinium

Dutta¹

2019

Mater. Res. Express

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Nonlocal quartic interactions and universality classes in perovskite manganites

Cited by 5 publications

References 47 publications

Comment on “Nonlocal quartic interactions and universality classes in perovskite manganites”

Comment on “Nonlocal quartic interactions and universality classes in perovskite manganites”

Magnetoelastic coupling and critical behavior of some strongly correlated magnetic systems

Lattice effects and the critical behavior of gadolinium

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