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Linking factors between groundstate pc in 2D iso- and anisotropic +/ - J Ising models

: Bendisch, J.


Physica. A 359 (2006), No.1-4, pp.399-414
ISSN: 0378-4371
Journal Article
Fraunhofer SCAI ()

For honeycomb, square and triangular lattices we consider the groundstate threshold pc of spontaneous absolute magnetization in iso- and anisotropic random +/-J Ising models from so-called uniform classes HCz,SQz,TRz. The class index z(1) gives a fixed number of so-called PAF-bonds on the plaquette perimeter. A PAF-bond is a bond which has a positive (P) probability p to be antiferromagnetic (AF) and the probability 1-p to be ferromagnetic where p has the same value for all the PAF-bonds in a considered lattice. The non-PAF-bonds in the lattice are ferromagnetic. In [Achilles et al., Physica A 275 (2000) 178], for each of the uniform classes HC1,...,HC6,SQ1,...,SQ4,TR1,...,TR3 we proposed a so-called basic minimal (maximal) model to obtain the minimal (maximal) pc-value in the underlying class. Moreover, supported by estimates from simulations, concerning these basic models, we gave presumably exact values for the minimal (maximal) pc. Here we show that the predicted pc -values are linked by meaningful factors. To this end, in essence, z-values (1,2,...,6) and coordination numbers (hc=3,sq=4,tr=6) are used. Typical factors are (sq-1)/(hc-1) or z1/z21. Especially, the minimal model case, with its 13 basic models fits in very well. Furthermore, for in-between-models of a uniform class, pc is approximated by linear interpolation between pc,min and pc,max from basic minimal and maximal models.