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We study Monte Carlo calculations of the effective potential for a scalarfield theory using three techniques. One of these is a new method proposed andtested for the first time. In each case we extract the renormalised quantitiesof the theory. The system studied in our calculations is a one component$\phi^4$ model in two dimensions. We apply these methods to both the weak andstrong coupling regime. In the weak coupling regime we compare our results forthe renormalised quantities with those obtained from two-loop latticeperturbation theory. Our results are verified in the strong coupling regimethrough comparison with the strong coupling expansion. We conclude thateffective potential methods, when suitably chosen, can be accurate tools incalculations of the renormalised parameters of scalar field theories.

Optimization of Monte Carlo calculations of the effective potential