Boundary critical behavior ofd=2 self-avoiding walks on correlated and uncorrelated vacancies

Numerical simulation of a lattice polymer model at its integrable point

“…For the sake of completeness we have also found estimates of the universal amplitude ratios A and B by fitting against a correction of n −4/7 , which provide consistent straight fit extrapolations A = 0.1534(10) and B = 0.475 (5) .…”

“…We hence plotted, in Figure 3, on a double-logarithmic scale the normalized partition function Z n /µ n bn versus the length n of the path. This allows us to estimate γ from straight line fits which we give as γ = 1.045 (5) . We point out that this estimate is positive while the conjectured value above in equation (3.4) is not.…”

“…There was debate at the time over the surface exponents which was resolved by Vanderzande et al [4] and Stella et. al [5] on the hexagonal lattice and on the square lattice by Foster et al [6].…”

Adsorptionlike Collapse of Diblock Copolymers

“…On the other hand, the A and B monomers are not segregated, and their alternance in space resembles, to some extent, an antiferromagnetic microphase structure. By assuming ν c = 3/4, we can predict φ exactly in 2D, following a strategy of identification with geometric percolative objects, which in the past revealed extremely fruitful for homopolymer problems [6,15,16]. The idea is that the statistics of suitably chosen percolative contours could reproduce the critical behavior of interacting polymers in the conditions of interest.…”

“…The idea is that the statistics of suitably chosen percolative contours could reproduce the critical behavior of interacting polymers in the conditions of interest. The homopolymer at the theta point in 2D is known to have the same statistics as the external perimeter (hull) of a critical percolation cluster [17], and this coincidence is at the basis of the full exact characterization of theta scaling [6,15,16]. On square lattice, the incipient infinite cluster of the percolation problem for elementary squares ( only squares with an edge in common are connected) is expected to have an externally accessible hull which, besides assuming the configurations of a self-avoiding ring, has the statistical fractal dimension D c1 = 1/ν SAW = 4/3 of a swollen SAW [18].…”