The collapse transition of self-avoiding walks on a square lattice: A computer simulation study

Abstract

Employing the scanning simulation method, we study the tricritical behavior (at the Flory θ point) of self-avoiding walks with nearest-neighbors attraction energy ε(−‖ε‖) on a square lattice. We obtain −ε/kBTt=0.658±0.004, where Tt is the tricritical temperature and kB is the Boltzmann constant. The radius of gyration G and the end-to-end distance R lead to νt(G)=0.5795±0.0030 and νt(R) =0.574±0.006, respectively. We also obtain γt=1.11±0.022 and μt =3.213±0.013, where γt is the free energy exponent and μt is the growth parameter. Three estimates are calculated for the crossover exponent φt , based, respectively, on G, R and the specific heat C: φt (G)=0.597±0.008, φt(R)=0.564±0.009, and φt(C)=0.66±0.02. Our values for νt and γt are close to the Duplantier and Saleur exact values for the θ′ point, νt =4/7=0.571... and γt=8/7=1.142 ... . However, our values of φt are significantly larger than the exact value φt=3/7=0.42... . This suggests that the θ and θ′ points belong to different universality classes.

Surface critical exponents of self-avoiding walks and trails on a square lattice: The universality classes of the θ and θ’ points

“…A related question, raised by Shapir and Oono [14], concerns the universality class of trails, which are walks with a weaker excluded-volume restriction than that of SAWs [15]. They have argued that at tricriticality (unlike at infinite temperature) trails and SAWs may belong to different classes [16][17][18][19][20].The numerical results for the 0 point (i.e., for SAWs with nn attractions) and for tricritical trails mostly agree with the DS value v= j while the values for 7 are slightly smaller than the DS value f. On the other hand, the central values for <p are larger than the DS value f -0.43 (see and references cited therein); for the most reliable Monte Carlo studies they range from 0.48 to 0.60 for SAWs [12,21,22] and from 0.68 to 0.80 for trails [17,18]. This suggests that the 0 and 0' points and trails belong to different universality classes.…”

Microcanonical simulations of adsorbing self-avoiding walks

“…The success of the implementation suggests that this numerical method may be used on other models (collapsing self-avoiding walks [30,39], for example). However, it may be necessary to extend the method by introducing, in addition to the sets of parameters denoted by {β ,u } and {γ ,u }, additional sets of parameters which are conjugate to classes of elementary moves.…”

A combinatorial algorithm for effective generation of long maximally compact lattice chains

“…4 To illustrate with an example, Meirovich and Lim report simulations on a square lattice in which attrition coefficient decays from 0.80 for N ϭ 60 to 0.16 for Nϭ220. 6 Monte Carlo schemes are often equipped with enrichment techniques in order to generate longer walks. Some common enrichment schemes for improving the acceptance fraction are the method of strides 7 and the s-p enrichment 8 technique.…”