Paul Balduf#paperOfTheDay is "Accurate critical exponents for Ising like systems in non-integer dimensions" from 1987. This is one out of a sequence of articles with very similar titles and similar sets of authors, appearing over several years with updated numerical values.
The basic scheme is to use perturbative #quatumFieldTheory in 4-epsilon dimensions to compute critical exponents of the Ising model. This produces a power series in epsilon, which is then, in principle, evaluated at epsilon=1 in order to compute values for the physically interesting dimension 3 (computing directly in D=3 dimensions is less accurate because there, the quartic coupling is relevant, and therefore the theory is strongly interacting, whereas the expansion around 4 dimensions describes a weakly interacting system).
Of course, the power series in epsilon is divergent, therefore it would be inaccurate to simply substitute epsilon=1 (in the truncated series). Instead, one computes a Borel transform of the series data, conformally maps to the complex unit disk, and computes a Laplace integral from 0 to 1 (this is a widely known standard method for resummation of this type of divergent series). Here, the authors additionally introduce three free parameters, which they tune to improve numerical accuracy. The output is a table of resummed critical exponents between 1.5 and 4 dimensions in small steps.
Today, we know 8-loop data instead of 4, which gives rise to much more accurate values, but the basic picture has not changed much.
#physics
https://jphys.journaldephysique.org/articles/jphys/abs/1987/01/jphys_1987__48_1_19_0/jphys_1987__48_1_19_0.html
The basic scheme is to use perturbative #quatumFieldTheory in 4-epsilon dimensions to compute critical exponents of the Ising model. This produces a power series in epsilon, which is then, in principle, evaluated at epsilon=1 in order to compute values for the physically interesting dimension 3 (computing directly in D=3 dimensions is less accurate because there, the quartic coupling is relevant, and therefore the theory is strongly interacting, whereas the expansion around 4 dimensions describes a weakly interacting system).
Of course, the power series in epsilon is divergent, therefore it would be inaccurate to simply substitute epsilon=1 (in the truncated series). Instead, one computes a Borel transform of the series data, conformally maps to the complex unit disk, and computes a Laplace integral from 0 to 1 (this is a widely known standard method for resummation of this type of divergent series). Here, the authors additionally introduce three free parameters, which they tune to improve numerical accuracy. The output is a table of resummed critical exponents between 1.5 and 4 dimensions in small steps.
Today, we know 8-loop data instead of 4, which gives rise to much more accurate values, but the basic picture has not changed much.
#physics
https://jphys.journaldephysique.org/articles/jphys/abs/1987/01/jphys_1987__48_1_19_0/jphys_1987__48_1_19_0.html