<i>Introduction to the Renormalization Group and to Critical Phenomena</i>

Pfeuty, P.; Toulouse, G.; Domany, Eytan

doi:10.1063/1.2994997

Cited by 123 publications

(152 citation statements)

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“…Comparing two length scales, for large N , we find that the mean-field theory breaks down very close to the critical point, i.e. for The shift, induced by fluctuations, is obtained in the one-loop approximation 6,7) .…”

Section: Introductionmentioning

confidence: 98%

“…(3.9) is described in detail in Ref. [6,7]. Here we use an expansion in the number of loops (Chapter 6, Ref.…”

Section: A Vertex Functions and Critical Pointmentioning

confidence: 99%

“…For T → T c and q → 0, we expect I −1 (0) ∼ (T /T c − 1) −γ , where γ = 1 in the mean-field theory 6,7) . The breakdown of this relation is usually used in experiment to estimate the Ginzburg region 7,8−13) and therefore, we also base the calculations of the Ginzburg region on the scattering intensity 14,15) .…”

Section: Introductionmentioning

confidence: 99%

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The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

Hołyst

Vilgis

1996

Macro Theory & Simulations

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The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers.The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chain close to critical points, fluctuations induced shift of phase boundaries. In particular

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Section: Introductionmentioning

confidence: 98%

“…(3.9) is described in detail in Ref. [6,7]. Here we use an expansion in the number of loops (Chapter 6, Ref.…”

Section: A Vertex Functions and Critical Pointmentioning

confidence: 99%

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The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

Hołyst

Vilgis

1996

Macro Theory & Simulations

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“…This creates a puzzle. Liquids governed by dispersion forces (decaying asymptotically ∼ r −6 with distance r) belong to the Ising universality class [10], i.e., the critical exponents describing the singular behavior of various thermodynamic quantities and structural properties are those of the Ising universality class. This also holds at interfaces.…”

Section: Introductionmentioning

confidence: 99%

“…where the critical exponents ν, β, and ∆ take the values of the Ising model (in d = 3: ν = 0.6301(4), β = 0.32653 (10), and ∆ = 3ν − β = 1.564 [11]). The latter universal singularity Γ ∼ |∆µ| −0.194 is weaker than the non-universal one Γ ∼ |∆µ| −1/3 for complete wetting [3], although according to the general renormalization group (RG) arguments the dispersion forces, which are responsible for this non-universal behavior, at first glance should give rise only to corrections to scaling (i.e., subdominant power laws).…”

Section: Introductionmentioning

confidence: 99%

Interplay of complete wetting, critical adsorption, and capillary condensation

et al. 2009

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The excess adsorption Γ in two-dimensional Ising strips (∞ × L) subject to identical boundary fields, at both one-dimensional surfaces decaying in the orthogonal direction j as −h1j −p , is studied for various values of p and along various thermodynamic paths below the critical point by means of the density-matrix renormalization-group method. The crossover behavior between the complete wetting and critical adsorption regimes, occurring in semi-infinite systems, are strongly influenced by confinement effects. Along isotherms T = const the asymptotic power law dependences on the external bulk field, which characterize these two regimes, are undercut by capillary condensation. Along the pseudo first-order phase coexistence line of the strips, which varies with temperature, we find a broad crossover regime where both the thickness of the wetting film and Γ increase as function of the reduced temperature τ but do not follow any power law. Above the wetting temperature the order parameter profiles are not slab-like but exhibit wide interfacial variations and pronounced tails. Inter alia, our explicit calculations demonstrate that, contrary to opposite claims by Kroll and Lipowsky [Phys. Rev. B 28, 5273 (1983)], for p = 2 critical wetting transitions do exist and we determine the corresponding wetting phase diagram in the (h1, T ) plane.

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Social Opinion Dynamics

Weisbuch

2006

Econophysics and Sociophysics

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Introduction to the Renormalization Group and to Critical Phenomena

Cited by 123 publications

References 0 publications

The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

Interplay of complete wetting, critical adsorption, and capillary condensation

Social Opinion Dynamics

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