The paradox of The Netherlands: Why a successful economy is struggling?

A. van Witteloostuijn, C. Hendriks

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review


For the hard-core lattice gas model defined on independent sets weighted by an activity λ, we study the critical activity λc(ℤ2) for the uniqueness threshold on the 2-dimensional integer lattice ℤ2. The conjectured value of the critical activity is approximately 3.796. Until recently, the best lower bound followed from algorithmic results of Weitz (2006). Weitz presented an FPTAS for approximating the partition function for graphs of constant maximum degree Δ when λ < λc(TΔ)λ < λc(TΔ) where TΔ is the infinite, regular tree of degree Δ. His result established a certain decay of correlations property called strong spatial mixing (SSM) on ℤ2 by proving that SSM holds on its self-avoiding walk tree Tsaw(ℤ2), and as a consequence he obtained that λc(Z2) ≥ λc(T4) = 1.675. Restrepo et al. (2011) improved Weitz’s approach for the particular case of ℤ2 and obtained that λc(ℤ2) > 2.388. In this paper, we establish an upper bound for this approach, by showing that SSM does not hold on Tsaw(ℤ2) when λ > 3.4. We also present a refinement of the approach of Restrepo et al. which improves the lower bound to λc(ℤ2) > 2.48.
Original languageEnglish
Title of host publicationThe Netherlands as an EU Member
Subtitle of host publicationAwkward or Loyal Partner?
EditorsA. Schout, J. Rood
Place of PublicationThe Hague / Portland, OR
PublisherEleven International Publishing
Number of pages312
ISBN (Print)9789490947996
Publication statusPublished - 2013


Dive into the research topics of 'The paradox of The Netherlands: Why a successful economy is struggling?'. Together they form a unique fingerprint.

Cite this