1996/07/11 by Philippe Di Francesco, P. Di Francesco, Emmanuel Guitter +3 · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Block Copolymer Self-Assembly #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physreve.55.237
published as Phys. Rev. E 55 (1997) 237-251 · uses harvmac (l), epsf, 17 figs included, uuencoded, tar compressed
arxiv created 1996/07/11 · openalex publication_date 1997/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of folding of the regular triangular lattice in the presence of a quenched random bending rigidity \ifmmode±\else\textpm\fiK and a magnetic field h (conjugate to the local normal vectors to the triangles). The randomness in the bending energy can be understood as arising from a prior marking of the lattice with quenched creases on which folds are favored. We consider three types of quenched randomness:m(i) a 'physical' randomness where the creases arise from some prior random folding; (ii) a Mattis-like randomness where creases are domain walls of some quenched spin system; (iii) an Edwards-Anderson-like randomness where the bending energy is \ifmmode±\else\textpm\fiK at random, independently on each bond. The corresponding (K,h) phase diagrams are determined in the hexagon approximation of the cluster variation method. Depending on the type of randomness, the system shows essentially different behaviors.