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We explore short-distance static correlation functions in the infinite XXZchain using previously derived formulae which represent the correlationfunctions in factorized form. We compute two-point functions ranging over 2, 3and 4 lattice sites as functions of the temperature and the magnetic field inthe massive regime $\Delta>1$, extending our previous results to the fullparameter plane of the antiferromagnetic chain ($\Delta > -1$ and arbitraryfield $h$). The factorized formulae are numerically efficient and allow fortaking the isotropic limit ($\Delta = 1$) and the Ising limit ($\Delta =\infty$). At the critical field separating the fully polarized phase from theN\'eel phase, the Ising chain possesses exponentially many ground states. Theresidual entropy is lifted by quantum fluctuations for large but finite$\Delta$ inducing unexpected crossover phenomena in the correlations.

Short-distance thermal correlations in the massive XXZ chain