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Copolymers near a Random Selective Interface

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 1974)

Abstract

In this chapter we consider a different version of the directed copolymer model analyzed in Chapter 9, namely, one where the linear interface is replaced by a random interface. In particular, rather than putting the oil and the water in two halfplanes, we place them in large square blocks in a random percolation-type fashion. This is a crude model of a copolymer in an emulsion, consisting of oil droplets floating in water (see Fig. 10.1). We will see that this model exhibits a remarkably rich critical behavior, with two phases in a supercritical percolation regime and four phases in a subcritical percolation regime. Large deviations and partial annealing estimates will again play a central role, together with coarse-graining, entropy estimates and variational calculus.

Keywords

  • Free Energy
  • Phase Diagram
  • Critical Curve
  • Tricritical Point
  • Block Pair

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Correspondence to Frank den Hollander .

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© 2009 Springer-Verlag Berlin Heidelberg

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Hollander, F.d. (2009). Copolymers near a Random Selective Interface. In: Random Polymers. Lecture Notes in Mathematics(), vol 1974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00333-2_10

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