Linking factors between groundstate pc in 2D iso and anisotropic +/  J Ising models
 Physica. A 359 (2006), Nr.14, S.399414 ISSN: 03784371 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer SCAI () 
Abstract
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 socalled uniform classes HCz,SQz,TRz. The class index z(1) gives a fixed number of socalled PAFbonds on the plaquette perimeter. A PAFbond is a bond which has a positive (P) probability p to be antiferromagnetic (AF) and the probability 1p to be ferromagnetic where p has the same value for all the PAFbonds in a considered lattice. The nonPAFbonds 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 socalled basic minimal (maximal) model to obtain the minimal (maximal) pcvalue 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, zvalues (1,2,...,6) and coordination numbers (hc=3,sq=4,tr=6) are used. Typical factors are (sq1)/(hc1) or z1/z21. Especially, the minimal model case, with its 13 basic models fits in very well. Furthermore, for inbetweenmodels of a uniform class, pc is approximated by linear interpolation between pc,min and pc,max from basic minimal and maximal models.