Griffiths singularities in unbinding of strongly disordered polymers

Area of Science:

• Statistical mechanics
• Polymer physics
• Condensed matter physics

Background:

• Heteropolymers with quenched disorder can exhibit complex phase behavior.
• Griffiths singularities are non-analyticities in thermodynamic functions arising from rare, favorable regions in disordered systems.
• Understanding these singularities is crucial for predicting material properties under varying conditions.

Purpose of the Study:

• To investigate Griffiths singularities in the context of strongly disordered heteropolymer unbinding.
• To introduce and analytically study a simplified model of heteropolymer binding energies.
• To determine the conditions and temperatures at which these singularities and other transitions occur.

Main Methods:

• Analytical study of a heteropolymer model with two random binding energies (-1 and -v).
• Utilizing Lee-Yang zeros of the partition sum to analyze phase transitions.
• Examining the behavior of the model in the limit of infinite binding energy difference (v → ∞) and for finite, large v.

Main Results:

• The model demonstrates a Griffiths-type singularity at a characteristic temperature T(G) = O(1) in the v → ∞ limit.
• This singularity corresponds to the melting of long, low-binding-energy homogeneous domains.
• For finite v >> 1, an additional unbinding transition is predicted at a higher temperature T(M) = O(v).

Conclusions:

• Griffiths singularities are a key feature in the unbinding of strongly disordered heteropolymers.
• The introduced model provides a framework for understanding these singularities and associated transitions.
• The findings suggest a rich phase diagram for disordered heteropolymers, with distinct transitions dependent on binding energy distributions.