  Monte Carlo data simulating phase transitions in Ising strips $D\times L,$
($D\llL) $ with periodic boundary conditions show that $T_{c}(D)=0$ for $D\leq
D^{\ast}\simeq 6$ and $0<T_{c}(D)<T_{c}(d=2)$ for $D>D^{\ast}.$ Regular scaling
of $ML^{\beta /\nu}$ vs $|T-T_{c}|L^{1/\nu}$ is obtained only for $%
D>D^{\ast}$and the Monte Carlo effective susceptibility critical exponent
$\gamma_{eff} (D)$ is shown to be well described by $\gamma (d)=\beta
(d)[\delta (d)-1]$ with $% d_{eff}(D)$ given by $d_{eff}(D)\simeq
1.5+({1/200})(D-6)$ and $\beta (d)=(\frac{3d%}{16}-{1/4}),$ $\delta
^{-1}(d)=(\frac{2d}{15}-{1/5})$, which can be understood as valid with
$d_{eff}(D)$.
