What is integrability of discrete variational systems?

@article{Boll2014WhatII,
title={What is integrability of discrete variational systems?},
author={R. Boll and M. Petrera and Y. Suris},
journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
year={2014},
volume={470}
}

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries… Expand