Critical behavior of compressible magnets

Sak, J.

doi:10.1103/physrevb.10.3957

Cited by 127 publications

(66 citation statements)

References 18 publications

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“…Indeed, there are general nonperturbative theoretical arguments indicating that the only stable FP in 3D may be the Bose one and the phase transitions of interest should be governed by that stable FP [15]. However, up to now this assertion found no confirmation within the RG approach.…”

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confidence: 82%

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Mudrov

Varnashev

2001

Jetp Lett.

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Within the four-loop ε expansion, we study the critical behavior of certain antiferromagnets with complicated ordering. We show that an anisotropic stable fixed point governs the phase transitions with new critical exponents. This is supported by the estimate of critical dimensionality N C c = 1.445(20) obtained from six loops via the exact relation N C c = 1 2 N R c established for the real and complex hypercubic models.

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mentioning

confidence: 82%

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Mudrov

Varnashev

2001

Jetp Lett.

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“…The numerical estimates obtained via transformation (16) are collected in Table II. The critical exponents for the isotropic and Bose FPs are also presented, for comparison.…”

Section: Critical Exponents and Conclusionmentioning

confidence: 99%

“…The point is that when v = z, the model (1) describes n interacting Bose systems. As was shown by Sak [16], the interaction term can be represented as the product of the energy operators of various two-component subsystems. It was also found that one (the smallest) of the eigenvalue exponents characterizing the evolution of this term under the renormalization group in a neighborhood of the Bose FP is proportional to the specific heat exponent α.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, we put the stability of the result of processing with respect to variation of a and b into the foundation of our approach to resummation of divergent series 8 [28]. The parameter λ is chosen from the condition of the most rapid convergence of the series (16), that is from minimizing the quantity |1 − F l (ε;a,b) F l−1 (ε;a,b) |, where l is the step of truncation and F l (ε; a, b) is the l-partial sum for F (ε; a, b). If both eigenvalues are negative, the FP is infrared stable and the critical behavior of experimental systems undergoing second-order phase transitions is determined only by that stable point.…”

Section: Introductionmentioning

confidence: 99%

“…An appropriate resummation procedure has to be applied, in order to extract reliable physical information from them. To obtain the eigenvalues estimates, we have used an approach based on the Borel-Leroy transformation (16) modified with the conformal mapping z = √ x+1−1 √ x+1+1 [25,26], which does not require the knowledge of the exact asymptotic high-order behavior of the series [28]. The coefficients A k (λ) are determined from the equality B(x(z)) = A(λ,z)…”

Section: Introductionmentioning

confidence: 99%

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Critical behavior of certain antiferromagnets with complicated ordering: Four-loopɛ-expansion analysis

Mudrov

Varnashev

2001

Phys. Rev. B

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The critical behavior of a complex N -component order parameter Ginzburg-Landau model with isotropic and cubic interactions describing antiferromagnetic and structural phase transitions in certain crystals with complicated ordering is studied in the framework of the four-loop renormalization group (RG) approach in (4 − ε) dimensions. By using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced and resummed by the Borel-Leroy transformation combined with a conformal mapping. Investigation of the global structure of RG flows for the physically significant cases N = 2 and N = 3 shows that the model has an anisotropic stable fixed point governing the continuous phase transitions with new critical exponents. This is supported by the estimate of the critical dimensionality N c = 1.445(20) obtained from six loops via the exact relation N c = 1 2 n c established for the complex and real hypercubic models.

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Strain effects on the microphase separation in interpenetrating polymer networks and cross‐linked polymer mixtures

Stepanow

Frisch

1995

Macro Theory & Simulations

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SUMMARY:We study the microphase separation in cross-linked polymer mixtures and interpenetrating polymer networks by taking into account the coupling between the fluctuations of the order parameter and the strain tensor. We predict that thermal fluctuations of the order parameter decrease the compression and shear moduli and that compression of the sample decreases the critical temperature of microphase separation. We also compute the scattering function in the case of shear and uniaxial deformations.The microphase separations in polymer systems such as block copolymers cross-linked polymers 6,7) and interpenetrating polymer networks (IPNs) 8-13) are of current interest in the literature. TWO chemically different, incompatible polymers A and B d o not completely segregate because they are kept together by cross-links, but can segregate on some scale r* -2 x /q*. de Gennes6) proposed a description of the microphase separation based on an electrostatic analogy. According to this idea the appearance of a nonzero value of the order parameter @ ( r ) (charge density) is accompanied by a local polarization P ( r ) representing the elastic forces due to the cross-links. The latter is connected with the charge density as follows divP(r) = -@ ( r )The effective Hamiltonian (in units of KT) is given by H = 1 dd r& with where x is the Flory-Huggins interaction parameter, x, is its critical value at which the phase separation occurs, and e = a2/(24p). de Gennes estimated the elasticity constant c as c = 36/(pnR2), with n being the number of monomer units between two consecutive cross-links, and R2 = nu2 being the mean square distance between two consecutive cross-links. p is the average density of the network. Here we consider the most symmetric case, i. e. parameters such as n and a being the same for both polymers

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Critical behavior of compressible magnets

Cited by 127 publications

References 18 publications

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Critical behavior of certain antiferromagnets with complicated ordering: Four-loopɛ-expansion analysis

Strain effects on the microphase separation in interpenetrating polymer networks and cross‐linked polymer mixtures

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