Griffiths singularities in unbinding of strongly disordered polymers

TL;DR

This paper investigates Griffiths singularities in the unbinding process of strongly disordered heteropolymers using an analytical model with randomly distributed binding energies, revealing distinct transitions at different temperature regimes.

Contribution

It introduces a new analytical model for disordered heteropolymer unbinding and analyzes Griffiths singularities via Lee-Yang zeros, highlighting different unbinding transitions.

Findings

Griffiths singularity occurs at a temperature T_G in the limit v -> infinity.

An additional unbinding transition appears at high temperature T_M for finite v.

The model demonstrates melting of long homogeneous domains of low binding energy.

Abstract

Griffiths singularities occurring in the unbinding of strongly disordered heteropolymers are studied. A model with two randomly distributed binding energies -1 and -v, is introduced and studied analytically by analyzing the Lee-Yang zeros of the partition sum. It is demonstrated that in the limit v -> infinity the model exhibits a Griffiths type singularity at a temperature T_G =O(1) corresponding to melting of long homogeneous domains of the low binding energy. For finite v >> 1 the model is expected to exhibit an additional, unbinding, transition at a high temperature T_M=O(v).