New Monte Carlo algorithms for interacting self-avoiding walks

In this paper we present two new Monte Carlo algorithms for simulating interacting self-avoiding walks. These algorithms are built on the Berretti - Sokal and reptation algorithms for simulating non-interacting self-avoiding walks respectively by adding a Metropolis step. We enhance each algorithm by introducing special local moves. In addition, the reptation algorithm is further enhanced by running the simulations as a multiple Markov chain. Each of these algorithms are studied here through an analysis of their autocorrelation properties. In the case of the Berretti - Sokal algorithm an increase in efficiency by a factor of around 40 is achieved for non-interacting self-avoiding walks.