Elastic energy and phase structure in a continuous spin Ising chain with applications to chiral homopolymers

Abstract

We present a numerical Monte Carlo analysis of the phase structure in a continuous spin Ising chain that describes chiral homopolymers. We find that depending on the value of the Metropolis temperature, the model displays the three known nontrivial phases of polymers: At low temperatures the model is in a collapsed phase, at medium temperatures it is in a random walk phase, and at high temperatures it enters the self-avoiding random walk phase. By investigating the temperature dependence of the specific energy we confirm that the transition between the collapsed phase and the random walk phase is a phase transition, while the random walk phase and self-avoiding random walk phase are separated from each other by a crossover transition. We propose that the model can be applied to characterize the statistical properties of protein folding. For this we compare the predictions of the model to a phenomenological elastic energy formula, proposed by J. Lei and K. Huang [e-print arXiv:1002.5013; Europhys. Lett. 88, 68004 (2009)] to describe folded proteins.