2013/06/30 by Filippo Colomo, F. Colomo, A. G. Pronko · 41 citations
Mathematics · Physics and Astronomy · #Boundary (topology) #Combinatorics #Condensed matter physics #Eigenvalues and eigenvectors #Geometry #Mathematical analysis #Mathematics #Phase (matter) #Phase transition #Physics #Quantum mechanics #Random Matrices and Applications #Random matrix #Square (algebra) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Vertex (graph theory) #cond-mat.stat-mech #hep-th #math-ph #math.CO #math.MP
paper · pdf · doi:10.1103/physreve.88.042125
published in Physical Review E 88(4), 042125 (American Physical Society) · 21 pages, 6 figures; v3: journal version with misprints in text and Fig. 3 corrected; footnote added at page 3
openalex publication_date 2013/10/14 · arxiv created 2014/05/30 · arxiv updated 2014/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic square shape and given size and address the bulk properties of tilings as the size is varied. We observe that the free energy exhibits a third-order phase transition when the cut-off square, increasing in size, reaches the arctic ellipse-the phase separation curve of the original (unmodified) Aztec diamond. We obtain this result by studying the thermodynamic limit of a certain nonlocal correlation function of the underlying six-vertex model with domain wall boundary conditions, the so-called emptiness formation probability (EFP). We consider EFP in two different representations: as a τ function for Toda chains and as a random matrix model integral. The latter has a discrete measure and a linear potential with hard walls; the observed phase transition shares properties with both Gross-Witten-Wadia and Douglas-Kazakov phase transitions.