We study pairs of interacting self-avoiding walks ¿omega(1), omega(2)¿ on the 3d simple cubic lattice. They have a common origin omega(1)(0)=omega 20, and are allowed to overlap only at the same monomer position along the chain: omega(1)(i) not equal omega(2)(j) for i not equal j, while omega(1)(i)=omega(2)(i) is allowed. The latter overlaps are indeed favored by an energetic gain epsilon. This is inspired by a model introduced long ago by Poland and Sheraga [J. Chem. Phys. 45, 1464 (1966)] for the denaturation transition in DNA where, however, self avoidance was not fully taken into account. For both models, there exists a temperature T(m) above which the entropic advantage to open up overcomes the energy gained by forming tightly bound two-stranded structures. Numerical simulations of our model indicate that the transition is of first order (the energy density is discontinuous), but the analog of the surface tension vanishes and the scaling laws near the transition point are exactly those of a second-order transition with crossover exponent straight phi=1. Numerical and exact analytic results show that the transition is second order in modified models where the self-avoidance is partially or completely neglected.

We compute the thermodynamic properties of the glass phase in a binary mixture of soft spheres. Our approach is a generalization to mixtures of the replica strategy, recently proposed by Mezard and Parisi, providing a first principle statistical mechanics computation of the thermodynamics of glasses. The method starts from the inter-atomic potentials, and translates the problem into the study of a molecular liquid. We compare our analytical predictions to numerical simulations, focusing onto the values of the thermodynamic transition temperature and the configurational entropy.

We use results derived in the framework of the replica approach to study the liquid-glass thermodynamic transition. The main results are derived without using replicas and applied to the study of the Lennard-Jones binary mixture introduced by Kob and Andersen. We find that there is a phase transition due to the entropy crisis. We compute both analytically and numerically the value of the phase transition point T(K) and the specific heat in the low temperature phase.