J. Vannimenus

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Papers by J. Vannimenus

Interface entropy and phase transitions in frustrated ising systems

Journal de Physique Lettres, 1978

2014 L'annulation de l'énergie d'interface à T = 0 est compatible avec l'existence d'une transiti... more 2014 L'annulation de l'énergie d'interface à T = 0 est compatible avec l'existence d'une transition de phase à température finie, dans des systèmes de spins d'Ising. Dans des systèmes frustrés, la création d'une interface peut coûter de l'entropie. Cet effet peut suffire à entrainer une température de transition non nulle. Nous donnons un exemple explicite sur un modèle périodique et discutons quelques conséquences possibles pour les verres de spins d'Ising en deux dimensions. Abstract. 2014 It is pointed out that the vanishing of the interface energy at T = 0 is compatible with the existence of a phase transition at finite temperature in Ising systems. In frustrated systems an interface may cost entropy. This effect may be sufficient to produce a non-zero transition temperature. We give an explicit example of this behaviour on a periodic model. Some possible consequences for 2-D Ising spin-glasses are discussed.

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Finite‐size scaling and phenomenological renormalization (invited)

Journal of Applied Physics, 1982

Research in recent years has shown that combining finite‐size scaling theory with the transfer ma... more

Le Journal De Physique - Lettres

We show that two very different temperature regimes exist for problems of the travelling salesman... more We show that two very different temperature regimes exist for problems of the travelling salesman type, and that the annealed approximation is valid for the high-temperature regime. Random-link models are introduced, for which upper and lower bounds on the free energy are obtained in the low-temperature regime. A soluble model is presented, which possesses a phase transition strongly reminiscent of the spin-glass transition. Tome 45

Polymer adsorption : bounds on the cross-over exponent and exact results for simple models

Journal de Physique, 1989

2014 Nous donnons des bomes supérieure et inférieure pour l'exposant 03A6 de cross-over, dans le ... more 2014 Nous donnons des bomes supérieure et inférieure pour l'exposant 03A6 de cross-over, dans le problème de l'adsorption d'un polymère sur une surface attractive impénétrable. Ces bornes sont bien vérifiées pour des modèles exactement résolubles, où le polymère réside sur un réseau fractal. Dans l'un de ces modèles nous observons également un point multicrique, où une transition d'effondrement en volume coexiste avec une transition d'adsorption en surface. Une méthode simple de renormalisation dans l'espace réel est présentée pour le réseau carré, elle donne 03A6 = 0,48, en bon accord avec la valeur présumée exacte 03A6 = 1/2, qui coincide avec notre borne supérieure. Abstract. 2014 We provide an upper and a lower bound for the cross-over exponent 03A6 in polymer adsorption on an impenetrable attractive surface. These bounds are shown to be verified for exactly solvable models where the polymer resides on a fractal lattice. In one of these models we also find a multicritical point where a bulk collapse transition and a surface adsorption transition coexist. A simple real-space renormalization scheme is presented for the square lattice, it gives 03A6 = 0.48, in close agreement with the presumably exact value 1/2, which coincides with our upper bound.

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The Art of Walking on Fractal Spaces and Random Media

Springer Proceedings in Physics, 1985

Since we know that mountain shapes are natural fractals, the title would be appropriate for a lec... more Since we know that mountain shapes are natural fractals, the title would be appropriate for a lecture on climbing the Mont Blanc, the Aiguille Verte or any of the peaks we can contemplate from Les Houches. My subject is more down to earth and only consists in a short review of recent work on different types of walks on fractal lattices and on random systems such as percolation clusters. The first part is a reminder of geometrical and physical aspects of dimensionality, and discusses why several dimensions are needed to characterize fractal objects. The second part is devoted to “simple” walks, mainly random walks, and gives a short account of classical diffusion and conduction in random media. Several reviews of these aspects have appeared recently, by ALEXANDER |1|, MITESCU and ROUSSENQ |2|, RAMMAL |3| and AHARONY |4|, and the reader is referred to these papers for deeper discussions and for technical points. The following parts deal with “advanced” walks, where additional rules are specified: this leads to a large variety of problems and to a wealth of new physical effects. The examples include random walks in the presence of traps, biased walks (e.g., dispersion of particles in a flow through a porous medium), selfavoiding walks. For all these problems, the lack of translational invariance of the lattice (fractal or random) introduces new features, and even the simplest situations may provide surprises.

The Phenomenological Renormalization Method

Springer Series in Synergetics, 1981

One aim of the study of critical phenomena is the calculation of the exponents which describe the... more One aim of the study of critical phenomena is the calculation of the exponents which describe the singularities of the thermodynamic functions at a second order phase transition point. Most of the models of statistical mechanics are not solvable exactly, therefore these exponents are only known approximatively. The three main approaches which allow to calculate the critical exponents are the series expansions, the Monte Carlo methods and the renormalization group theories. The phenomenological renormalization method which was introduced by NIGHTINGALE [1] is a real space renormalization method. The philosophy of the method is to use the fact that one can calculate exactly the thermodynamic properties of one dimensional systems and then from this information obtain the critical properties of systems in higher dimension. Its main advantages are: 1) the method can be used for a large class of models, 2) it gives satisfactory results which can be improved systematically, 3) only one parameter is renormalized.

Static electronic perturbations of metallic surfaces

Physical Review B, 1975

We present a theory of charge distributions induced at a jellium surface by a static applied pote... more We present a theory of charge distributions induced at a jellium surface by a static applied potential. Exact expressions are derived for the changes in surface potential, and the total potential barrier in terms of the unperturbed electron distribution and the change in the latter due to adding electrons to the jellium. These results are applied to a simple chemisorption model and the induced dipole moment is calculated as a function of proton position for several r, values.

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Topological Defects and Disordered Systems

Polymers, Liquid Crystals, and Low-Dimensional Solids, 1984

The first and most obvious evolution in the study of defects in ordered systems is toward a much ... more The first and most obvious evolution in the study of defects in ordered systems is toward a much greater diversity, but it is counterbalanced by a powerful effort toward unification. The diversity stems from the experimental study of new materials, such as the liquid heliums, liquid crystals, or two-dimensional systems. These materials contain defects which play an important physical role, and are different from the well-known defects of metals and semiconductors. On the other hand, recent theoretical work based on topological concepts has restored unity by providing deeper understanding and a broader framework that includes many a priori unrelated cases (though not all the old classics!). The topological theory also leads to the prediction of new phenomena and makes contact with other fields of physics where similar concepts are used (e.g., solitons or monopoles may be viewed as defects). Here is a beautiful example of how progress occurs in physics!

Anatomy of the Frustrated Xy Model

Ground-state morphology of random frustrated XY systems

Physical Review B, 1989

ABSTRACT

Sum-rules and the surface energy of metals

Solid State Communications, 1974

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Thermal effects in sandwich structures

Solid State Communications, 1971

Abstract An exact solution is given to the usual model for electro-thermal switching in amorphous... more

Self-consistent calculation of the forces between two metallic half spaces

Solid State Communications, 1975

A simple model of the forces between two pieces of the same metals is solved self-consistently wi... more A simple model of the forces between two pieces of the same metals is solved self-consistently within a local density-functional approximation for the total energy. The results are compared with a recent calculation of non-local Van der Waals forces and the implications for the surface energy of metals are discussed.

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On the connection between spin glasses and gauge field theories

Physics Reports, 1980

A simple connection between Ising spin glasses and the Z 2 lattice gauge theory, at negative plaq... more A simple connection between Ising spin glasses and the Z 2 lattice gauge theory, at negative plaquette temperatures, is presented. It is first shown that annealed models give useful lower bounds on the free energy and ground-state energy of spin glasses. However, they have unphysical low temperature properties (e.g. a negative entropy), which are related to a temperature dependence of the frustration. A restricted annealing scheme is presented which remedies this deficiency through the introduction of a pure gauge coupling counterterm. The possible phase diagrams of the lattice gauge system and their relevance to spin glass transitions are discussed.

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$Research paper thumbnail of The collapse transition of linear polymers on fractal lattices$

The collapse transition of linear polymers on fractal lattices

Journal of Physics A: Mathematical and General, 1987

The authors show that for linear polymers a collapse transition exists on several fractal lattice... more The authors show that for linear polymers a collapse transition exists on several fractal lattices and obtain exact results for the critical exponents at this transition. A 'rod-like' phase is found in some cases at intermediate temperatures, between the swollen phase and the collapsed phase. They introduce infinitesimal recursion relations with correlation function rescaling as the formal limit of a class of fractals, which give a better approximation to Euclidean 2D lattices. The gyration radius exponent at the transition temperature lies in the range nu 1=0.546+or-0.010, in good agreement with a recent transfer matrix calculation. The possible relevance of anisotropy at the collapse transition is discussed.

Contact angle on heterogeneous surfaces: Weak heterogeneities

Journal of Colloid and Interface Science, 1985

ABSTRACT

Electron energy distributions from GaP with negative electron affinity. I. Emission properties of thermalized electrons

Journal of Applied Physics, 1977

Photoelectron energy distributions are measured on negative electron affinity (NEA) GaP (100) sur... more Photoelectron energy distributions are measured on negative electron affinity (NEA) GaP (100) surfaces for near-band-gap photon energy as a function of the activation conditions with Cs or Cs and O2. X electrons in NEA GaP have a low escape probability unless Cs-O activation is used and the work function reduced to less than 1 eV. Measured energy distribution curves are

Numerical study of the square Ising frustration model

Journal of Applied Physics, 1979

Ground state correlations in the Ising model with random ± J bonds are investigated on a square l... more Ground state correlations in the Ising model with random ± J bonds are investigated on a square lattice, as a function of the concentration of negative bonds. By comparing all the ground‐states of (18×18) samples, we study the size distribution of packets of solitary spins. Large packets, containing more than half the spins, are observed in most samples, even at maximum bond disorder. This finding implies a remarkable rigidity of the random frustrated system at zero temperature.

Essential Singularity in a Model of Branched Polymers

Europhysics Letters (EPL), 1987

We study the asymptotic properties of large branched polymers (lattice animals) on a fractal latt... more We study the asymptotic properties of large branched polymers (lattice animals) on a fractal lattice, the two-dimensional modified Sierpinski gasket of base b = 3. The generating function displays an essential singularity of the form G(x) ∼ exp [c(xc - x)-ψ], with ψ = ln(3 - √3)/ln(3 + √3) ≃ 0.1527. This is in contrast to the power law singularity found for periodic lattices and some other fractal lattices such as the standard Sierpinski gasket. This result suggests that similar essential singularities may also exist for polymers in nonhomogeneous media.

Modulated phase of an ising system with competing interactions on a Cayley tree

Zeitschrift f�r Physik B Condensed Matter, 1981

A system with competing nearest-neighbour and next-nearest-neighbour interactions is considered o... more A system with competing nearest-neighbour and next-nearest-neighbour interactions is considered on a Cayley tree. The phase diagram contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature. The variation of the wavevector with temperature in the modulated phase is studied in detail, it shows narrow commensurate steps between incommensurate regions (“incomplete devil's staircase”). The behaviour of the coherence length near the different transitions is also analyzed.

Interface entropy and phase transitions in frustrated ising systems

Journal de Physique Lettres, 1978

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Finite‐size scaling and phenomenological renormalization (invited)

Journal of Applied Physics, 1982

Research in recent years has shown that combining finite‐size scaling theory with the transfer ma... more

Le Journal De Physique - Lettres