Simple model for the DNA denaturation transition.

摘要: We study pairs of interacting self-avoiding walks ${{\mathit{\ensuremath{\omega}}}^{1},{\mathit{\ensuremath{\omega}}}^{2}}$ on the $3d$ simple cubic lattice. They have a common origin ${\mathit{\ensuremath{\omega}}}_{0}^{1}={\mathit{\ensuremath{\omega}}}_{0}^{2},$ and are allowed to overlap only at same monomer position along chain: ${\mathit{\ensuremath{\omega}}}_{i}^{1}\ensuremath{\ne}{\mathit{\ensuremath{\omega}}}_{j}^{2}$ for $i\ensuremath{\ne}j,$ while ${\mathit{\ensuremath{\omega}}}_{i}^{1}={\mathit{\ensuremath{\omega}}}_{i}^{2}$ is allowed. The latter overlaps indeed favored by an energetic gain \ensuremath{\epsilon}. This inspired model introduced long ago Poland Sheraga [J. Chem. Phys. 45, 1464 (1966)] denaturation transition in DNA where, however, self avoidance was not fully taken into account. For both models, there exists temperature ${T}_{m}$ above which entropic advantage open up overcomes energy gained forming tightly bound two-stranded structures. Numerical simulations our indicate that first order (the density discontinuous), but analog surface tension vanishes scaling laws near point exactly those second-order with crossover exponent $\ensuremath{\varphi}=1.$ exact analytic results show second modified models where self-avoidance partially or completely neglected.