flatIGW — An inverse algorithm to compute the density of states of lattice self avoiding walks

Abstract

a b s t r a c tWe show that the Density of States (DoS) for lattice Self Avoiding Walks can be estimated by using an inverse algorithm, called flatIGW, whose step-growth rules are dynamically adjusted by requiring the energy histogram to be locally flat. Here, the (attractive) energy associated with a configuration is taken to be proportional to the number of non-bonded nearest neighbor pairs (contacts). The energy histogram is able to explicitly direct the growth of a walk because the step-growth rule of the Interacting Growth Walk [5]) samples the available nearest neighbor sites according to the number of contacts they would make. We have obtained the complex Fisher zeros corresponding to the DoS, estimated for square lattice walks of various lengths, and located the θ temperature by extrapolating the finite size values of the real zeros to their asymptotic value, ∼1.49 (reasonably close to the known value, ∼1.50 (Barkema et al. (1998) [14]).

The Θ points of interacting self-avoiding walks and rings on a 2D square lattice

“…We have employed Hayes' method [24] in our exact enumeration algorithm (we have taken rooted SAWs [24] in our enumeration process). We test our method by using C N,m obtained from Monte Carlo estimates for longer walk lengths [30].…”

Phase transitions in a linear self-interacting polymer on FCC lattice using flat energy interacting growth walk algorithm

“…A random variation of β G between −β max G and +β max G ensures a uniform accumulation of energy histogram, and is the flatIGW algorithm which generates walks having flat energy histogram [20,21].…”

“…We note that, all SAWs up to walk length 24 have been enumerated on the FCC lattice [15], however there is no information about DoS, and therefore the data cannot be used to study coil-globule transition. One of us employed a flat histogram Interacting Growth Walk (flatIGW, see section 2 for a description of the algorithm) to study the coil-globule phase transitions in two dimensional lattices [20,21]. Furthermore, flatIGW is able to obtain almost exact DoS for short ISAWs on SC lattice [22].…”

Transições ele fase em um modelo de crescimento interagente semiflexível

“…O eventual mapeamento entre este modelos, aliado ao comportamento termodinâmico similar, justifica uso do IGW para analisar, ao menos de forma qualitativa, o comportamento de cadeias auto-interagentes sob diferentes temperaturas. O estabelecimento dos critérios de mapeamento destes modelos constituiárea ativa de pesquisa e, recentemente, o IGW foi utilizado com sucesso na geração da densidade de estados de modelos ISAW [29].…”

“…Os critérios de mapeamento discutidos por Narasimham e cols. [13,29] não foram utilizados neste trabalho. Aqui, o modelo de crescimento interagente de original de Narasimhan e cols.…”