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Abstract
Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex (6V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a s × n square lattice (s ≤ n). In this paper, we derive the analytic expression of the arctic curve, for a = b = 1 and c=2 (Δ= 0), while keeping the ratio s/n ϵ [0, 1] as a free parameter. The computation relies on the tangent method. We also consider domino tilings of double Aztec rectangles and show via the tangent method that, for particular parameters, the arctic curve is identical to that of the 6V model with partial DWBC. Our results are confirmed by extensive numerical simulations.
Original language | English |
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Article number | 305004 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 55 |
Issue number | 30 |
DOIs | |
Publication status | Published - 29 Jul 2022 |
Keywords
- arctic phenomenon
- domino tilings
- double Aztec rectangle
- integrable lattice model
- six-vertex model
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Dive into the research topics of 'Arctic curves of the 6V model with partial DWBC and double Aztec rectangles'. Together they form a unique fingerprint.Projects
- 1 Finished
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Reaction-diffusion processes on temporal and non-normal networks
de Kemmeter, J. & Carletti, T.
1/10/20 → 30/09/22
Project: Research
Equipment
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High Performance Computing Technology Platform
Benoît Champagne (Manager)
Technological Platform High Performance ComputingFacility/equipment: Technological Platform