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We examine the N=2 Wess-Zumino model defined on the $d=2$ Euclidean latticein connection with a restoration of the Leibniz rule in the limit $a\to0$ inperturbatively finite theory. We are interested in the difference between theWilson and Ginsparg-Wilson fermions and in the effects of extra interactionsintroduced by an analysis of Nicolai mapping. As for the Wilson fermion, itinduces a linear divergence to individual tadpole diagrams in the limit$a\to0$, which is absent in the Ginsparg-Wilson fermion. This divergencesuggests that a careful choice of lattice regularization is required in areliable numerical simulation. As for the effects of the extra couplingsintroduced by an analysis of Nicolai mapping, the extra couplings do notcompletely remedy the supersymmetry breaking in correlation functions inducedby the failure of the Leibniz rule in perturbation theory, though thosecouplings ensure the vanishing of vacuum energy arising from disconnecteddiagrams. Supersymmetry in correlation functions is recovered in the limit$a\to 0$ {\em with or without} those extra couplings. In the context of latticetheory, it may be properly said that supersymmetry does not improve ultravioletproperties but rather it is well accommodated in theories with good ultravioletproperties.Comment: 24 pages. A reference was added. Appeared in Phys. Rev. D66 (2002)  07451

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>Wess-Zumino model on the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>Euclidean lattice

N=2Wess-Zumino model on thed=2Euclidean lattice