Some rigorous results on majority rule renormalization group transformations near the critical point

DOI10.1007/BF01048038zbMath1096.82513MaRDI QIDQ2499844

Tom Kennedy

Publication date: 23 August 2006

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

majority ruleLattice spin systemrigorous high-temperature phase

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Renormalization group methods in equilibrium statistical mechanics (82B28) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (11)

Renormalizing the renormalization group pathologies ⋮ Conformal invariance of isoheight lines of the \((2+1)\)-dimensional Wolf-Villain surfaces ⋮ Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory ⋮ Renormalization group maps for Ising models in lattice-gas variables ⋮ Absence of renormalization group pathologies near the critical temperature. Two examples ⋮ Effect of the block-spin configuration on the location of \(\beta_c\) in two-dimensional Ising models ⋮ Renormalization group at criticality and complete analyticity of constrained models: A numerical study ⋮ Some numerical results on the block spin transformation for the 2D Ising model at the critical point. ⋮ Pathological behavior of renormalization-group maps at high fields and above the transition temperature. ⋮ Ill-defined block-spin transformations at arbitrarily high temperatures. ⋮ A cluster expansion approach to renormalization group transformations

Cites Work

• The Dobrushin-Shlosman phase uniqueness criterion and applications to hard squares
• A fixed-point equation for the high-temperature phase of discrete lattice spin systems.
• Regularity properties and pathologies of position-space renormalization-group transformations

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