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Numerical computations in strongly-interacting quantum field theories areoften performed using Monte-Carlo sampling methods. A key task in thesecalculations is to estimate the value of a given physical quantity from thedistribution of stochastic samples that are generated using the Monte-Carlomethod. Typically, the sample mean and sample variance are used to define theexpectation values and uncertainties of computed quantities. However, theMonte-Carlo sample distribution contains more information than these basicproperties and it is useful to investigate it more generally. In this work, theexact form of the probability distributions of two-point correlation functionsat zero momentum in O(N) lattice field theories in the disordered phase and ininfinite volume are determined. These distributions allow for a robustinvestigation of the efficacy of the Monte-Carlo sampling procedure and areshown also to allow for improved estimators of the target physical quantity tobe constructed. The theoretical expectations are shown to agree with numericalcalculations in the O(2) model.

Correlation function distributions for O(N) lattice field theories in the disordered phase