Effect of disorder in magnetic and biological systems

Using replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes, and a generalization of Schneider and Pytte model to the l-component classical spin vector model are presented. In the first model, we study the effects of global fluctuations of the surface normal to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been predicted by Bensimon et al and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order. In the second model, effects of a Gaussian random field on the phase transition of the l-component classical spin vector model are investigated. The phase diagrams are obtained in the cases l=1 and l=3, in opposite to what has been predicted by Schneided and Pytte. The results we obtain, for l=1 and l=3 show that the model exhibits a second-order, tricritical point and a first-order transition depending on the value of the =random field.Using replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes, and a generalization of Schneider and Pytte model to the l-component classical spin vector model are presented. In the first model, we study the effects of global fluctuations of the surface normal to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been predicted by Bensimon et al and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order. In the second model, effects of a Gaussian random field on the phase transition of the l-component classical spin vector model are investigated. The phase diagrams are obtained in the cases l=1 and l=3, in opposite to what has been predicted by Schneided and Pytte. The results we obtain, for l=1 and l=3 show that the model exhibits a second-order, tricritical point and a first-order transition depending on the value of the =random field

Stretching an heteropolymer

We study the influence of some quenched disorder in the sequence of monomers on the entropic elasticity of long polymeric chains. Starting from the Kratky-Porod model, we show numerically that some randomness in the favoured angles between successive segments induces a change in the elongation versus force characteristics, and this change can be well described by a simple renormalisation of the elastic constant. The effective coupling constant is computed by an analytic study of the low force regime.Comment: Latex, 7 pages, 3 postscript figur

Phase diagram of randomly polymerized membrane

Using a replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes is presented. In this model we study the effects of global fluctuations of the surface normals to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been predicted by Bensimon et al. and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order