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

J. Bendisch

Physica A: Statistical Mechanics and its Applications, 2006, vol. 359, issue C, 399-414

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 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 (Δhc=3,Δsq=4,Δtr=6) are used. Typical factors are (Δsq-1)/(Δhc-1) or z1/z2⩾1. 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.

Keywords: Random 2D Ising spin glasses; Groundstate phase transitions; Minimal matchings of frustrated plaquettes (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437105005698
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:359:y:2006:i:c:p:399-414

DOI: 10.1016/j.physa.2005.04.043

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().