A universal emulator for planar Ising lattices
Abstract
We introduce the notion of an Ising emulator for two-dimensional Ising models: a broad class of flat, unit-edge-length lattices can be represented as site- or bond-diluted supercells of a single host lattice, for which the Feynman--Vdovichenko/Kac--Ward solution is fixed once and for all. We construct explicit square and triangular emulators and show that a single transition matrix, supplemented by lattice-specific binary masks, gives all the thermodynamic quantities of interest for both ferro- and antiferromagnetic couplings. We apply the framework to all eleven Archimedean lattices, to all twenty 2-uniform lattices -- whose thermodynamics is obtained here for the first time -- and to several pentagonal lattices, and show that the same construction extends directly to fractal and disordered Ising models, with no modification to the underlying machinery.
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BibTeX
@misc{zinati2026universal,
title = {{A universal emulator for planar Ising lattices}},
author = {Riccardo Ben Alì Zinati and Alessandro Codello},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.05308},
eprint = {2607.05308},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05308},
}
RIS
TY - UNPB
TI - A universal emulator for planar Ising lattices
AU - Riccardo Ben Alì Zinati
AU - Alessandro Codello
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2607.05308
UR - https://arxiv.org/abs/2607.05308
AB - We introduce the notion of an Ising emulator for two-dimensional Ising models: a broad class of flat, unit-edge-length lattices can be represented as site- or bond-diluted supercells of a single host lattice, for which the Feynman--Vdovichenko/Kac--Ward solution is fixed once and for all. We construct explicit square and triangular emulators and show that a single transition matrix, supplemented by lattice-specific binary masks, gives all the thermodynamic quantities of interest for both ferro- and antiferromagnetic couplings. We apply the framework to all eleven Archimedean lattices, to all twenty 2-uniform lattices -- whose thermodynamics is obtained here for the first time -- and to several pentagonal lattices, and show that the same construction extends directly to fractal and disordered Ising models, with no modification to the underlying machinery.
ER -