  A disciplinary profile of a country is defined as the versor whose components
are the numbers of articles produced in a given discipline divided the overall
production of the country. Starting from the Essential Science Indicators (ESI)
schema of classification of subject area, we obtained the yearly disciplinary
profiles of a worldwide graph, where on each node sits a country, in the two
time intervals [1980-1988] and [1992-2017], the fall of the Berlin Wall being
the watershed. We analyse the empirical pairwise cross-correlation matrices of
the time series of disciplinary profiles. The contrast with random matrix
theory proves that, beyond measurement noise, the empirical cross-correlation
matrices bring genuine information. Arising from the Shannon theorem as the
least-structured model consistent with the measured pairwise correlations, the
stationary probability distribution of disciplinary profiles can be described
by a Boltzmann distribution related to a generalized $n_d$-dimensional
Heisenberg model. The set of network interactions of the Heisenberg model have
been inferred and to it they have been applied two clusterization methods,
hierarchical clustering and principal component analysis. On a geopolitical
plane this allow to obtain a characterization of the worldwide bilateral
interactions based on physical modeling. A simple geopolitical analysis reveals
the consistency of the results obtained and gives a boost to deeper historical
analysis. In order to obtain the optimal set of pairwise interactions we used a
Pseudo-Likelihood approach. We analytically computed the Pseudo-Likelihood and
its gradient. The analytical computations deserve interest in whatever
inference Bayesian problem involving a $n_d$-dimensional Heisenberg model.
