A convenient possibility is to use Monte Carlo (MC) algorithms, to sample the full partition function integral expressed in field-theoretic representation.
However, it is well known that MC sampling in conjunction with the basic field-theoretic representation of the partition function integral, directly obtained via the Hubbard-Stratonovich transformation, is impracticable, due to the so-called numerical sign problem (Baeurle 2002, Fredrickson 2002).
The difficulty is related to the complex and oscillatory nature of the resulting distribution function, which causes a bad statistical convergence of the ensemble averages of the desired structural and thermodynamic quantities.
They could convincingly demonstrate that this strategy provides an additional boost in the statistical convergence of the desired ensemble averages (Baeurle 2002).
Other promising field-theoretic simulation techniques have been developed recently, but they either still lack the proof of correct statistical convergence, like e.g. the Complex Langevin method (Ganesan 2001), and/or still need to prove their effectiveness on systems, where multiple saddle points are important (Moreira 2003).