Critical behavior of magnetic polymers in two and three dimensions.

We explore the critical behavior of two- and three-dimensional lattice models of polymers in dilute solution where the monomers carry a magnetic moment which interacts ferromagnetically with near-neighbor monomers. Specifically, the model explored consists of a self-avoiding walk on a square or cubic lattice with Ising spins on the visited sites. In three dimensions we confirm and extend previous numerical work, showing clearly the first-order character of both the magnetic transition and the polymer collapse, which happen together. We present results in two dimensions, where the transition is seen to be continuous. Finite-size scaling is used to extract estimates for the critical exponents and the transition temperature in the absence of an external magnetic field.

Elasticity of a DNA chain dotted with bubbles under force.

The flexibility and the extension along the direction of the force are shown to be related to the bubble number fluctuation and the average number of bubbles, respectively, when the strands of the DNA are subjected to a force along the same direction, here called a stretching force. The force-temperature phase diagram shows the existence of a tricritical point, where the first-order force-induced zipping transition becomes continuous. On the other hand, when the forces are being applied in opposite directions, here called an unzipping force, the transition remains first order, with the possibility of vanishing of the low-temperature reentrant phase for a semiflexible DNA. Moreover, we found that the bulk elasticity changes only if an external force penetrates the bound phase and affects the bubble states.

Softening of DNA near melting as disappearance of an emergent property.

Near the melting transition the bending elastic constant κ, an emergent property of double-stranded DNA (dsDNA), is shown not to follow the rodlike scaling for small-length N. The reduction in κ with temperature is determined by the denatured bubbles for a continuous transition, e.g., when the two strands are Gaussian, but by the broken bonds near the open end in a Y-like configuration for a first-order transition as for strands with excluded volume interactions. In the latter case, a lever rule is operational, implying a phase coexistence although dsDNA is known to be a single phase.