Oriented Polymers: A Transfer Matrix Calculation

TL;DR

This paper uses transfer matrix and finite size scaling methods to analyze oriented polymers, revealing critical exponents, a spiral transition under attraction, and differences in fractal dimensions compared to standard self-avoiding walks.

Contribution

It introduces a transfer matrix approach to study oriented polymers, identifying a spiral transition and computing fractal dimensions in various regimes.

Findings

Critical exponents match recent predictions.

Polymer undergoes a spiral transition with strong attraction.

Fractal dimension differs at spiral and collapse transitions.

Abstract

Based on transfer matrix techniques and finite size scaling, we study the oriented polymer (self-avoiding walk) with nearest neighbor interaction. In the repulsive regime, various critical exponents are computed and compared with exact values predicted recently. The polymer is also found to undergo a spiral transition for sufficiently strong attractive interaction. The fractal dimension of the polymer is computed in the repulsive, attractive regimes and at the spiral transition point. The later is found to be different from that at the collapse transition of ordinary self-avoiding walk.