Crossover between special and ordinary transitions in random semi-infinite Ising-like systems

Usatenko, Z.; Hu, Chin‐Kun

doi:10.1103/physreve.68.066115

Cited by 6 publications

(7 citation statements)

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“…The surface critical behaviour of the three-dimensional Ising model with quenched bulk disorder has been investigated both at the ordinary [263,264] and at the special transition point [263,265], using different renormalization group techniques. The crossover behaviour between these two transitions was studied recently in [266]. Interestingly, modified surface critical behaviour is encountered independently whether quenched surface disorder is present or not.…”

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 99%

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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Abstract. In the past perfect surfaces have been shown to yield a local critical behaviour that differs from the bulk critical behaviour. On the other hand surface defects, whether they are of natural origin or created artificially, are known to modify local quantities. It is therefore important to clarify whether these defects are relevant or irrelevant for the surface critical behaviour.The purpose of this review is two-fold. In the first part we summarise some of the important results on surface criticality at perfect surfaces. Special attention is thereby paid to new developments as for example the study of surface critical behaviour in systems with competing interactions or of surface critical dynamics. In the second part the effect of surface defects (presence of edges, steps, quenched randomness, lines of adatoms, regular geometric patterns) on local critical behaviour in semi-infinite systems and in thin films is discussed in detail. Whereas most of the defects commonly encountered are shown to be irrelevant, some notable exceptions are highlighted. It is shown furthermore that under certain circumstances non-universal local critical behaviour may be observed at surfaces.

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Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 99%

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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“…In the case of investigation the crossover behavior from the adsorbed to the non-adsorbed states (see [26,37,51]), an additional surface related term arises,…”

Section: Analysis Of Callan-symanzik Equationsmentioning

confidence: 99%

“…(3.17 The asymptotic scaling critical behavior of the correlation functions near the multicritical point can be obtained through a detailed analysis of the CS equations, as was proposed in [49,52] and employed in the case of the semi-infinite systems in [26,37,51,53,54]. Using the above mentioned scheme, the asymptotic scaling form of the surface correlation functions for long-flexible polymer chains with one end fixed at the surface and the other end located somewhere in the layer z above the surface can be written as…”

Section: Analysis Of Callan-symanzik Equationsmentioning

confidence: 99%

“…where η sp ⊥ = (η + η sp )/2 is the surface critical exponent which characterizes the critical point correlations perpendicular to the surface, Φ = ν(1 + η c(v * , w * )) is the surface crossover critical exponent [26,37,51] which characterizes the deviation from the multicritical point and x denotes r or z in G or G ⊥ which correspond to G (0,2) and G (1,1) functions, respectively.…”

Section: Analysis Of Callan-symanzik Equationsmentioning

confidence: 99%

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The influence of long-range correlated surface and near surface disorder on the process of adsorption of long-flexible polymer chains

Usatenko

Sommer

2007

J. Stat. Mech.

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The process of adsorption on a planar wall of long-flexible polymer chains in the medium with quenched long-range correlated disorder is investigated. We focus on the case of correlations between defects or impurities that decay according to the power-low x −a for large distances x, where x = (r, z). Field theoretical approach in d = 4 − ǫ and directly in d = 3 dimensions up to one-loop order for the semi-infinite |φ| 4 m-vector model (in the limit m → 0) with a planar boundary is used. The whole set of surface critical exponents at the adsorption threshold T = T a , which separates the nonadsorbed region from the adsorbed one is obtained. Moreover, we calculate the crossover critical exponent Φ and the set of exponents associated with them. We perform calculations in a double ǫ = 4 − d and δ = 4 − a expansion and also for a fixed dimension d = 3, up to one-loop order for different values of the correlation parameter 2 < a ≤ 3.The obtained results indicate that for the systems with long-range correlated quenched disorder the new set of surface critical exponents arises. All the surface critical exponents depend on a. Hence, the presence of long-range correlated disorder influences the process of adsorption of long-flexible polymer chains on a wall in a significant way.

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“…should be calculated at the infrared-stable 'pure' fixed point. The asymptotic scaling critical behaviour of the correlation functions can be obtained through a detailed analysis of the CS equations, as was proposed in [26,27] and employed in the case of the semi-infinite systems in [21,30], [33]- [35]. Integration of equations for β(v), η(v), η sp 1 (v) and η c(v) gives the asymptotic dependences…”

Section: The Modelmentioning

confidence: 99%