An integer Lipschitz height function on a graph assigns an integer to each vertex
such that the absolute value of the height difference
is at most 1 across every edge. Boundary
values may be fixed and an admissible function sampled
uniformly or with a weight. On the triangular lattice,
a weighted zero-boundary model assigns probability proportional to 
, where 
counts unordered adjacent pairs with unequal heights.
Integer Lipschitz Height Function
See also
Dirichlet Boundary Conditions, Gaussian Free Field, Lipschitz Function, Real Lipschitz Height Function, Triangular LatticeExplore with Wolfram|Alpha
References
Glazman, A. and Lammers, P. "Delocalisation and Continuity in 2D: Loop
, Six-Vertex, and Random-Cluster Models." Commun.
Math. Phys. 406, Article 108, 2025. https://doi.org/10.1007/s00220-025-05259-9.Peled,
R.; Samotij, W.; and Yehudayoff, A. "Grounded Lipschitz Functions on Trees Are
Typically Flat." Electron. Commun. Probab. 18, Article 55, 1-9,
2013. https://doi.org/10.1214/ECP.v18-2796.
Cite this as:
Weisstein, Eric W. "Integer Lipschitz Height Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IntegerLipschitzHeightFunction.html