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For short-range correlated disorder, the central limit theorem yields ∆T ∝ ξ −d/2 ∝ T dν⊥ /2 . Thus, a clean critical point is perturbatively stable, if the clean critical exponents fulfill the inequality T dν⊥ /2 < T for T → 0. 91). Critical systems have been divided into three categories according to the response of a pure system for quenched disorder • Irrelevant disorder : The critical behavior is unchanged, the macroscopic variables are self-averaging (the relative width of their probability distributions vanishes as L → ∞).

2). As we can see the universality classes of static models are split by the dynamical exponents. 4 Crossover between classes A model with some additional condition like an external field, surface ... may exhibit different universal scaling behavior by varying the parameters (in the field theoretical language (see Sect. 1 By tuning the control parameters close to these points we may see corrections to scaling. In terms of scaling forms, crossover phenomena are described by additional relevant scaling fields, characterized by a so-called crossover exponent [Riedel and Wegner (1969)].

1997); Sch¨ utz (2001)]. However fermionic field theories are much more difficult to solve. They involve non-commutative, Grassmann algebra and since near a transition to the absorbing state (which is very common in nonequilibrium models) the particle density is very low, they are expected to be equivalent to the bosonic theories. 62) April 4, 2008 9:14 World Scientific Book - 9in x 6in Introduction universality 15 and in the path integral formalism [Peliti (1985)] one can introduce a partition function over fields φ(x, t) and “response fields” ψ(x, t) with the statistical weight e−S(φ,ψ) .

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