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Given a set of variables and the correlations among them, we develop a method for finding clustering among the variables. The method takes advantage of information implicit in higher-order (not just pairwise) correlations. The idea is to define a Potts model whose energy is based on the correlations. Each state of this model is a partition of the variables and a Monte Carlo method is used to identify states of lowest energy, those most consistent with the correlations. A set of the 100 or so lowest such partitions is then used to construct a stochastic dynamics (using the adjacency matrix of each partition) whose observable representation gives the clustering. Three examples are studied. For two of them the 3$^mathrm{rd}$ order correlations are significant for getting the clusters right. The last of these is a toy model of a biological system in which the joint action of several genes or proteins is necessary to accomplish a given process.
A calculation method for higher-order moments of physical quantities, including magnetization and energy, based on the higher-order tensor renormalization group is proposed. The physical observables are represented by impurity tensors. A systematic s
We investigate the order of the topological quantum phase transition in a two dimensional quadrupolar topological insulator within a thermodynamic approach. Using numerical methods, we separate the bulk, edge and corner contributions to the grand pot
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of the pairin
Thermal transport in classical fluids is analyzed in terms of a Higher-Order Generalized Hydrodynamics (or Mesoscopic Hydro-Thermodynamics), that is, depending on the evolution of the energy density and its fluxes of all orders. It is derived in term
A concept of higher order neighborhood in complex networks, introduced previously (PRE textbf{73}, 046101, (2006)), is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each higher order