Series study of random animals in general dimensions

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Abstract
We construct general-dimension series for the random animal problem up to 15th order. These represent an improvement of five terms in four dimensions and above and one term in three dimensions. These series are analyzed, together with existing series in two dimensions, and series for the related Yang-Lee edge problem, to obtain accurate estimates of critical parameters, in particular, the correction to scaling exponent. There appears to be excellent agreement between the two models for both dominant and correction exponents.