Adsorption in models of ideal polymer chains on fractal spaces

Yang - Lee edge singularity on a class of tree-like lattices

“…It is tempting, therefore, to see whether this coincidence persists for all values of p. Our calculation [16], which follows the lines of Ref. [13], shows that this is, really, the case (ν c = ν G ).…”

“…In this Letter we develop an approach which allows us to obtain the exact closed-form expressions for the edge exponents of Ising models on finitely ramified fractal lattices. It turns out that relevant recursion relations themselves have a singular behavior near the YL edge fixed point, which is reminiscent of a singular structure of corresponding mappings appearing in some recently studied Gaussian models [13][14][15].…”

Oscillatory behavior of critical amplitudes of the Gaussian model on a hierarchical structure

“…where S i is the continuous spin variable at site i, K = J/k B T where T is temperature and J represents interaction between each nearest-neighbor pair of Gaussian spins, while < ij > denotes the summation over all such pairs. As we have shown in a previous paper [5], the rth order partition function can be expressed in terms of three parameters A (r) , B (r) , and D (r) which obey a set of recursion relations and suitable initial conditions. These relations are somewhat cumbersome (see Eqs.…”

“…Let us note, nevertheless, that they have a singular structure near the relevant fixed point, which does not allow us to make a common fixed-point analysis. As detailed in [5], for the critical value K c = 0.227 148 . .…”

“…In the near past a considerable research activity has been devoted to the studies of recursion relations which have a singular structure near the pertinent fixed points [1][2][3][4][5][6]. It was found that, under certain conditions, these singularities can lead to an unusual critical behavior of relevant physical quantities.…”