Exact Ground States of the Kaya-Berker Model

TL;DR

This study uses an exact polynomial-time algorithm to analyze the two-dimensional Kaya-Berker model, revealing a critical point at p_c=0.6423 and showing no stable spin-glass phase, contrasting prior non-exact results.

Contribution

First exact ground-state analysis of the Kaya-Berker model for large systems, providing precise critical point and clarifying the absence of a spin-glass phase.

Findings

Critical point p_c=0.6423(3) identified.

No thermodynamic stable spin-glass phase found.

Large system sizes up to 777^2 lattice sites analyzed.

Abstract

Here we study the two-dimensional Kaya-Berker model, with a site occupancy p of one sub lattice, by using a polynomial-time exact ground-state algorithm. Thus, we were able to obtain T=0 results in exact equilibrium for rather large system sizes up to 777^2 lattice sites. We obtained sub-lattice magnetization and the corresponding Binder parameter. We found a critical point p_c=0.6423(3) beyond which the sub-lattice magnetization vanishes. This is clearly smaller than previous results which were obtained by using non-exact approaches for much smaller systems. We also created for each realization minimum-energy domain walls from two ground-state calculations for periodic and anti-periodic boundary conditions, respectively. The analysis of the mean and the variance of the domain-wall distribution shows that there is no thermodynamic stable spin-glass phase, in contrast to previous claims about this model.